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#1
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Interest calculations.
Here in UK, banks seeking depositors must (for comparison purposes)
quote the AER (Annual Equivalent Rate) for each type of account they offer. So that although interest may be earned daily the AER tells us what the accrued daily interest will total in a year's time. Thus £2,000 invested on Jan.1st in an account offering 5.5% AER will have £110 added a year later. I wish to know what interest my deposit will have earned should I close the account early. So: In A1 I put the sum deposited. In A2 I put the AER (as a percentage). In A3 I put the number of days the money will have been in the account. What must I put in A4 to calculate the interest I might expect? TIA for any (all) reply (replies). As an old dog, slow at learning new tricks, I regard you who answer our questions on this ng as geniuses! -- DB. |
#2
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Interest calculations.
On Apr 12, 8:24*pm, "DB." wrote:
* * Here in UK, banks seeking depositors must (for comparison purposes) quote the AER (Annual Equivalent Rate) for each type of account they offer. *So that although interest may be earned daily the AER tells us what the accrued daily interest will total in a year's time. *Thus £2,000 invested on Jan.1st in an account offering 5.5% AER will have £110 added a year later. * * I wish to know what interest my deposit will have earned should I close the account early. *So: In A1 I put the sum deposited. In A2 I put the AER (as a percentage). In A3 I put the number of days the money will have been in the account. What must I put in A4 to calculate the interest I might expect? TIA for any (all) reply (replies). *As an old dog, slow at learning new tricks, I regard you who answer our questions on this ng as geniuses! -- DB. As AER is compounded daily, the daily interest is the 365th root of the AER, i.e. DailyInterest^(365)=AER. So your formula in A4 should read =A1*(A2^(A3/365)), if in A2 your AER is expressed as a multiplier (ie 5.5% = 1.055). If the cell is formatted as a percentage, then you need =A1*((A2+1)^(A3/365)) Put in days=365 to check that this works and gives the AER. Hope this helps |
#3
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Interest calculations.
I'm sure there are shorter answers. But this is an answer fron Norman Harker. That's different stuff!
-- Kind regards, Niek Otten Microsoft MVP - Excel By Norman Harker Here's a very long post but I hope the content will assist all those who struggle with these interest conversion calculation problems. It gives the basic details, sets out the 10 formulas and provides 10 User Defined Functions. *** Introduction *** Every profession has basic tools. Interest conversion formulas are the basic tools of investment analysis without which very little can be achieved in terms of performing the tasks or interpreting results. So be patient with the length of this posting as it aims at giving you the tools of the trade in a form that will involve the least pain and suffering. With interest conversion tools at hand your financial skills in Excel will go up many notches at once both in terms of what you can do and in terms of understanding what results you are getting. One of the great advantages of Excel is that tasks that were previously only reasonably capable of being performed by mathematics adepts can now be achieved by those who understand the principles only and don't want or need to juggle with formulas. But even the mathematics adepts can find life is a lot easier if they have standard formula re-expressions handy, or better, if they are in the form of ready to hand functions. Excel gives us these powers but they are not in a very user friendly form and at present, only those with knowledge and skills in financial maths are able to get the greatest use out of the program. *** Definitions *** There are two commonly quoted interest regimes: 1. APR (Annual Percentage Rate) or 'Nominal' 2. Effective Under the APR regime an interest rate is quoted in annual terms and *should* be quoted together with a compounding frequency per year. In calculating the interest the annual rate is divided by the compounding frequency and that rate is applied to the number of periods calculated in terms of the frequency. Thus if we use the commonly quoted APR(12) at (say) 6%, a rate of 6%/12 = 0.5% is applied to the number of months involved in the calculation. Under the Effective regime an interest rate is quoted together with the period for which it is effective. Thus we might quote a rate of 5% per annum effective or 0.25% per month effective. Legislative and customary usage can cause confusion. Where a rate is merely labeled 'APR' you should assume (pending check of 'small print') that it is the APR(12) or more correctly described 'Nominal compounded monthly' rate. Similarly, we might see '7% effective' quoted and here we should assume (pending check of 'small print') that this in an annual effective rate. It should be clear that the effective rate is a more 'truthful' rate. Where Nominal and Effective quoted rates are the same, the impact of compounding is such that the Nominal rate produces more interest than the Effective rate. Similarly, for the same quoted level of rate a Nominal rate with a higher frequency of compounding produces more interest that one with a lower frequency of compounding. One rate, the Annual Effective Rate, is special. It is the only rate which has the same absolute level under both regimes; 6% per annum effective is the same as 6% Nominal compounded once per year. For this reason, financial calculators and Excel conversion routines and algorithms make a lot of use of the annual effective rate for conversions between regimes. Caution! Legislators have been at work in many countries in the area of forcing declarations of interest in lending and leasing documents and advertisements. Would you believe that there are cases where the legislators have stuffed up the definitions? In the UK, for example, original legislation on truth in lending required the quotation of a rate to be labeled 'APR' and then went on to give a perfect definition of the Annual Effective Rate! I'm not sure whether or not this has been changed or whether they have had to live with the error. Further, you do need to look at the fine print of the legislation because frequently there is a requirement for the statutory rate quotation to take account of various fees and charges and assumptions on term of lease or loan. You will need to use the basic principles set out here, but the calculations will be much more complex. *** Principle of Equivalence *** Any interest rate compounded at one frequency can be expressed as being equivalent to another interest rate compounded at another frequency. Using a simple example: 5% per half year effective is equivalent to (1+0.05)^2 -1 = 10.25% per annum effective. We can use similar compound interest formulas and re-expressions to calculate equivalent rates to any quoted rate. We can express many different quotations of interest rates in terms of a common equivalent. Usually, that common equivalent will be the Annual Effective rate, but often custom or 'Truth in Lending' legislation will require expression in terms of the APR(12); better described as the Annual Nominal Compounded Monthly. *** Concept of Conversion between Nominal and Effective Regimes *** There are 10 Interest Rate Conversions commonly required although we can boil them down to the solution of a common equation of equivalence: (1+Nomx/Freqx)^Freqx = (1+Nomy/Freqy)^Freqy Nomx and Nomy are Nominal (APR) rates compounded at frequencies per year of x and y. Effx and Effy are Effective rates for frequencies of compounding per year of x and y. It's very important to note that where Freqx (or Freqy) is 1, then Nomx/Freqx or (Nomy/Freqy) is the Annual Effective Rate. This leaves now leads in to the formulas required for interest rate conversion: *** Interest Rate Conversion Formulas *** If we regard Annual Effective as a "Special" rate there are no less than 10 commonly required Interest Rate Conversions. Therein lays the cause of the common confusion. Here they are together with the formulas: 1 Effx_Nomx Effective for frequency to Nominal for Same Frequency = Effx * Freqx 2 Nomx_AnnEff Nominal for frequency to Annual Effective = (1 + Nomx / Freqx) ^ Freqx - 1 3 AnnEff_Nomx Annual Effective to Nominal = Freqx * ((1 + AnnEff) ^ (1 / Freqx) - 1) 4 Nomx_Effx Nominal for frequency to Effective for same Frequency = Nomx / Freqx 5 Effx_AnnEff Effective for frequency to Annual Effective = (1 + Effx) ^ Freqx - 1 6 Effx_Nomy Effective for frequency to Nominal for a different frequency = Freqy * ((1 + Effx) ^ (Freqx / Freqy) - 1) 7 Effx_Effy Effective for frequency to Effective for different frequency = (1 + Effx) ^ (Freqx / Freqy) - 1 8 Nomx_Nomy Nominal for a frequency to Nominal for a different frequency = Freqy * ((1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1) 9 Nomx_Effy Nominal for a frequency to Effective for a different frequency = (1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1 10 AnnEff_Effx Annual Effective to Effective for a frequency = (1 + AnnEff) ^ (1 / Freqx) - 1 Those are the essential tools of most basic financial calculations. If you understand those, you are way ahead of the pack and incidentally you've just broken through the first pain barrier of financial analysis. These 10 conversions can be shown on a diagram that illustrates the overall scheme of conversions: AnnEff Nomx Nomy Effx Effy That diagram with pretty connecting arrows and a table of Excel formulas, UDF functions and Sharp Financial Calculator routines brings understanding to 100% of students in 2 hours of tutorial plus 1 hour private study. Before I introduced it, there was much wailing and gnashing of teeth. There were abysmal levels of understanding after about 12 hours of "teaching" and endless hours of padded cell torture. We now have 10 hours extra for generating more understanding and applications (and students have more time for B & B). *** Interest Rate Conversion Functions *** Since interest rate conversions are required so often and are often nested within other functions, I find the following User Defined Functions are pretty essential and I have derived a systematic approach to their naming and ordering of the function arguments that are intended make their use very easy. But first, here are the 10 User Defined Functions: 1 EFFECTIVE FOR FREQUENCY TO NOMINAL FOR SAME FREQUENCY Function Effx_Nomx(Effx As Double, Freqx As Double) As Double Effx_Nomx = Effx * Freqx End Function 2 NOMINAL TO ANNUAL EFFECTIVE Function Nomx_AnnEff(Nomx As Double, Freqx As Double) As Double Nomx_AnnEff = (1 + Nomx / Freqx) ^ Freqx - 1 End Function 3 ANNUAL EFFECTIVE TO NOMINAL Function AnnEff_Nomx(AnnEff As Double, Freqx As Double) As Double AnnEff_Nomx = Freqx * ((1 + AnnEff) ^ (1 / Freqx) - 1) End Function 4 NOMINAL FOR FREQUENCY TO EFFECTIVE FOR SAME FREQUENCY Function Nomx_Effx(Nomx As Double, Freqx As Double) As Double Nomx_Effx = Nomx / Freqx End Function 5 EFFECTIVE FOR FREQUENCY TO ANNUAL EFFECTIVE Function Effx_AnnEff(Effx As Double, Freqx As Double) As Double Effx_AnnEff = (1 + Effx) ^ Freqx - 1 End Function 6 EFFECTIVE FOR FREQUENCY TO NOMINAL FOR DIFFERENT FREQUENCY Function Effx_Nomy(Effx As Double, Freqx As Double, Freqy As Double) As Double Effx_Nomy = Freqy * ((1 + Effx) ^ (Freqx / Freqy) - 1) End Function 7 EFFECTIVE FOR FREQUENCY TO EFFECTIVE FOR DIFFERENT FREQUENCY Function Effx_Effy(Effx As Double, Freqx As Double, Freqy As Double) As Double Effx_Effy = (1 + Effx) ^ (Freqx / Freqy) - 1 End Function 8 NOMINAL FOR FREQUENCY TO NOMINAL FOR DIFFERENT FREQUENCY Function Nomx_Nomy(Nomx As Double, Freqx As Double, Freqy As Double) As Double Nomx_Nomy = Freqy * ((1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1) End Function 9 NOMINAL FOR FREQUENCY TO EFFECTIVE FOR DIFFERENT FREQUENCY Function Nomx_Effy(Nomx As Double, Freqx As Double, Freqy As Double) As Double Nomx_Effy = (1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1 End Function 10 ANNUAL EFFECTIVE TO EFFECTIVE FOR FREQUENCY Function AnnEff_Effx(AnnEff As Double, Freqx As Double) As Double AnnEff_Effx = (1 + AnnEff) ^ (1 / Freqx) - 1 End Function What is the Logic that Allows Easy Choice and Naming of Function To use a function you need to be able to remember the name accurately. So naming, which we often relegate to a few seconds thought, is very important when there are 10 different functions for 10 different purposes. So I have derived and implemented a very simple algorithm for naming: 1. First I named the various rates and frequencies: Nomx and Nomy are Nominal (APR) rates compounded at the compounding frequencies per year of x and y. Effx and Effy are Effective rates for the frequencies of compounding per year of x and y Freqx and Freqy are required for arguments. They are the numeric values representing the number of compounding periods per year of Nomx and Nomy (two different Nominal (APR) rates). AnnEff is regarded as a special case, which indeed it is, because it is the only rate where the absulute level is the same for both Nominal and Effective. Nominal compounded 1 times per year *is* the annual effective rate. 2. This gives me my function name convention: RateYouHave_RateYouWant If there's only one species of Nominal rate (APR) or Effective rate then we use Nomx and Effx. Easy! I have Annual Effective. I want Nominal compounded monthly. Function name? AnnEff_Nomx I have a nominal rate compounded monthly (our common friend APR(12)) and I want the annual effective equivalent. Function name? Nomx_AnnEff What arguments are required and what order do they come in? 1. First argument is always the rate you have 2. Second argument is always freqx 3. If there is another frequency involved in the two rates (known + required) and if that frequency is not 1, then you need the third argument freqy. And that's all there is to it. With those formulas and functions you now have the base tools for a comprehensive range of calculations. A whole World of applications can now be developed. You are no longer constrained by simplifying assumptions that produce errors and distortions. And when you get results from Excel Functions and your applications, you can understand them and convert them to common bases for evaluation. For further and better explanations with examples including ones that integrate the functions in Excel financial functions see John Walkenbach's Excel 2002 Formulas. HTH -- Norman Harker Sydney, Australia Roll on Christmas 25th Dec and 7th Jan "DB." wrote in message ... | Here in UK, banks seeking depositors must (for comparison purposes) | quote the AER (Annual Equivalent Rate) for each type of account they | offer. So that although interest may be earned daily the AER tells us | what the accrued daily interest will total in a year's time. Thus | £2,000 invested on Jan.1st in an account offering 5.5% AER will have | £110 added a year later. | I wish to know what interest my deposit will have earned should I | close the account early. So: | In A1 I put the sum deposited. | In A2 I put the AER (as a percentage). | In A3 I put the number of days the money will have been in the account. | | What must I put in A4 to calculate the interest I might expect? | | TIA for any (all) reply (replies). As an old dog, slow at learning new | tricks, I regard you who answer our questions on this ng as geniuses! | | -- | DB. | | |
#4
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Interest calculations.
"Alex Simmons" wrote in message ... On Apr 12, 8:24 pm, "DB." wrote: Here in UK, banks seeking depositors must (for comparison purposes) quote the AER (Annual Equivalent Rate) for each type of account they offer. So that although interest may be earned daily the AER tells us what the accrued daily interest will total in a year's time. Thus £2,000 invested on Jan.1st in an account offering 5.5% AER will have £110 added a year later. I wish to know what interest my deposit will have earned should I close the account early. So: In A1 I put the sum deposited. In A2 I put the AER (as a percentage). In A3 I put the number of days the money will have been in the account. What must I put in A4 to calculate the interest I might expect? TIA for any (all) reply (replies). As an old dog, slow at learning new tricks, I regard you who answer our questions on this ng as geniuses! -- DB. As AER is compounded daily, the daily interest is the 365th root of the AER, i.e. DailyInterest^(365)=AER. So your formula in A4 should read =A1*(A2^(A3/365)), if in A2 your AER is expressed as a multiplier (ie 5.5% = 1.055). If the cell is formatted as a percentage, then you need =A1*((A2+1)^(A3/365)) Put in days=365 to check that this works and gives the AER. Hope this helps My, that was quick! Yes, it works (of course!) Very many thanks! From a reply to a recent posting here I've learned how to put in my deposit and withdrawal dates to calculate the 'days in' I'll need in cell A3 (above). I'm learning! -- DB. |
#5
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Interest calculations.
Thanks, Niek. That little lot is going to need some taking-in! I'm
going to be late to bed tonight! -- DB. "Niek Otten" wrote in message ... I'm sure there are shorter answers. But this is an answer fron Norman Harker. That's different stuff! -- Kind regards, Niek Otten Microsoft MVP - Excel By Norman Harker Here's a very long post but I hope the content will assist all those who struggle with these interest conversion calculation problems. It gives the basic details, sets out the 10 formulas and provides 10 User Defined Functions. *** Introduction *** Every profession has basic tools. Interest conversion formulas are the basic tools of investment analysis without which very little can be achieved in terms of performing the tasks or interpreting results. So be patient with the length of this posting as it aims at giving you the tools of the trade in a form that will involve the least pain and suffering. With interest conversion tools at hand your financial skills in Excel will go up many notches at once both in terms of what you can do and in terms of understanding what results you are getting. One of the great advantages of Excel is that tasks that were previously only reasonably capable of being performed by mathematics adepts can now be achieved by those who understand the principles only and don't want or need to juggle with formulas. But even the mathematics adepts can find life is a lot easier if they have standard formula re-expressions handy, or better, if they are in the form of ready to hand functions. Excel gives us these powers but they are not in a very user friendly form and at present, only those with knowledge and skills in financial maths are able to get the greatest use out of the program. *** Definitions *** There are two commonly quoted interest regimes: 1. APR (Annual Percentage Rate) or 'Nominal' 2. Effective Under the APR regime an interest rate is quoted in annual terms and *should* be quoted together with a compounding frequency per year. In calculating the interest the annual rate is divided by the compounding frequency and that rate is applied to the number of periods calculated in terms of the frequency. Thus if we use the commonly quoted APR(12) at (say) 6%, a rate of 6%/12 = 0.5% is applied to the number of months involved in the calculation. Under the Effective regime an interest rate is quoted together with the period for which it is effective. Thus we might quote a rate of 5% per annum effective or 0.25% per month effective. Legislative and customary usage can cause confusion. Where a rate is merely labeled 'APR' you should assume (pending check of 'small print') that it is the APR(12) or more correctly described 'Nominal compounded monthly' rate. Similarly, we might see '7% effective' quoted and here we should assume (pending check of 'small print') that this in an annual effective rate. It should be clear that the effective rate is a more 'truthful' rate. Where Nominal and Effective quoted rates are the same, the impact of compounding is such that the Nominal rate produces more interest than the Effective rate. Similarly, for the same quoted level of rate a Nominal rate with a higher frequency of compounding produces more interest that one with a lower frequency of compounding. One rate, the Annual Effective Rate, is special. It is the only rate which has the same absolute level under both regimes; 6% per annum effective is the same as 6% Nominal compounded once per year. For this reason, financial calculators and Excel conversion routines and algorithms make a lot of use of the annual effective rate for conversions between regimes. Caution! Legislators have been at work in many countries in the area of forcing declarations of interest in lending and leasing documents and advertisements. Would you believe that there are cases where the legislators have stuffed up the definitions? In the UK, for example, original legislation on truth in lending required the quotation of a rate to be labeled 'APR' and then went on to give a perfect definition of the Annual Effective Rate! I'm not sure whether or not this has been changed or whether they have had to live with the error. Further, you do need to look at the fine print of the legislation because frequently there is a requirement for the statutory rate quotation to take account of various fees and charges and assumptions on term of lease or loan. You will need to use the basic principles set out here, but the calculations will be much more complex. *** Principle of Equivalence *** Any interest rate compounded at one frequency can be expressed as being equivalent to another interest rate compounded at another frequency. Using a simple example: 5% per half year effective is equivalent to (1+0.05)^2 -1 = 10.25% per annum effective. We can use similar compound interest formulas and re-expressions to calculate equivalent rates to any quoted rate. We can express many different quotations of interest rates in terms of a common equivalent. Usually, that common equivalent will be the Annual Effective rate, but often custom or 'Truth in Lending' legislation will require expression in terms of the APR(12); better described as the Annual Nominal Compounded Monthly. *** Concept of Conversion between Nominal and Effective Regimes *** There are 10 Interest Rate Conversions commonly required although we can boil them down to the solution of a common equation of equivalence: (1+Nomx/Freqx)^Freqx = (1+Nomy/Freqy)^Freqy Nomx and Nomy are Nominal (APR) rates compounded at frequencies per year of x and y. Effx and Effy are Effective rates for frequencies of compounding per year of x and y. It's very important to note that where Freqx (or Freqy) is 1, then Nomx/Freqx or (Nomy/Freqy) is the Annual Effective Rate. This leaves now leads in to the formulas required for interest rate conversion: *** Interest Rate Conversion Formulas *** If we regard Annual Effective as a "Special" rate there are no less than 10 commonly required Interest Rate Conversions. Therein lays the cause of the common confusion. Here they are together with the formulas: 1 Effx_Nomx Effective for frequency to Nominal for Same Frequency = Effx * Freqx 2 Nomx_AnnEff Nominal for frequency to Annual Effective = (1 + Nomx / Freqx) ^ Freqx - 1 3 AnnEff_Nomx Annual Effective to Nominal = Freqx * ((1 + AnnEff) ^ (1 / Freqx) - 1) 4 Nomx_Effx Nominal for frequency to Effective for same Frequency = Nomx / Freqx 5 Effx_AnnEff Effective for frequency to Annual Effective = (1 + Effx) ^ Freqx - 1 6 Effx_Nomy Effective for frequency to Nominal for a different frequency = Freqy * ((1 + Effx) ^ (Freqx / Freqy) - 1) 7 Effx_Effy Effective for frequency to Effective for different frequency = (1 + Effx) ^ (Freqx / Freqy) - 1 8 Nomx_Nomy Nominal for a frequency to Nominal for a different frequency = Freqy * ((1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1) 9 Nomx_Effy Nominal for a frequency to Effective for a different frequency = (1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1 10 AnnEff_Effx Annual Effective to Effective for a frequency = (1 + AnnEff) ^ (1 / Freqx) - 1 Those are the essential tools of most basic financial calculations. If you understand those, you are way ahead of the pack and incidentally you've just broken through the first pain barrier of financial analysis. These 10 conversions can be shown on a diagram that illustrates the overall scheme of conversions: AnnEff Nomx Nomy Effx Effy That diagram with pretty connecting arrows and a table of Excel formulas, UDF functions and Sharp Financial Calculator routines brings understanding to 100% of students in 2 hours of tutorial plus 1 hour private study. Before I introduced it, there was much wailing and gnashing of teeth. There were abysmal levels of understanding after about 12 hours of "teaching" and endless hours of padded cell torture. We now have 10 hours extra for generating more understanding and applications (and students have more time for B & B). *** Interest Rate Conversion Functions *** Since interest rate conversions are required so often and are often nested within other functions, I find the following User Defined Functions are pretty essential and I have derived a systematic approach to their naming and ordering of the function arguments that are intended make their use very easy. But first, here are the 10 User Defined Functions: 1 EFFECTIVE FOR FREQUENCY TO NOMINAL FOR SAME FREQUENCY Function Effx_Nomx(Effx As Double, Freqx As Double) As Double Effx_Nomx = Effx * Freqx End Function 2 NOMINAL TO ANNUAL EFFECTIVE Function Nomx_AnnEff(Nomx As Double, Freqx As Double) As Double Nomx_AnnEff = (1 + Nomx / Freqx) ^ Freqx - 1 End Function 3 ANNUAL EFFECTIVE TO NOMINAL Function AnnEff_Nomx(AnnEff As Double, Freqx As Double) As Double AnnEff_Nomx = Freqx * ((1 + AnnEff) ^ (1 / Freqx) - 1) End Function 4 NOMINAL FOR FREQUENCY TO EFFECTIVE FOR SAME FREQUENCY Function Nomx_Effx(Nomx As Double, Freqx As Double) As Double Nomx_Effx = Nomx / Freqx End Function 5 EFFECTIVE FOR FREQUENCY TO ANNUAL EFFECTIVE Function Effx_AnnEff(Effx As Double, Freqx As Double) As Double Effx_AnnEff = (1 + Effx) ^ Freqx - 1 End Function 6 EFFECTIVE FOR FREQUENCY TO NOMINAL FOR DIFFERENT FREQUENCY Function Effx_Nomy(Effx As Double, Freqx As Double, Freqy As Double) As Double Effx_Nomy = Freqy * ((1 + Effx) ^ (Freqx / Freqy) - 1) End Function 7 EFFECTIVE FOR FREQUENCY TO EFFECTIVE FOR DIFFERENT FREQUENCY Function Effx_Effy(Effx As Double, Freqx As Double, Freqy As Double) As Double Effx_Effy = (1 + Effx) ^ (Freqx / Freqy) - 1 End Function 8 NOMINAL FOR FREQUENCY TO NOMINAL FOR DIFFERENT FREQUENCY Function Nomx_Nomy(Nomx As Double, Freqx As Double, Freqy As Double) As Double Nomx_Nomy = Freqy * ((1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1) End Function 9 NOMINAL FOR FREQUENCY TO EFFECTIVE FOR DIFFERENT FREQUENCY Function Nomx_Effy(Nomx As Double, Freqx As Double, Freqy As Double) As Double Nomx_Effy = (1 + Nomx / Freqx) ^ (Freqx / Freqy) - 1 End Function 10 ANNUAL EFFECTIVE TO EFFECTIVE FOR FREQUENCY Function AnnEff_Effx(AnnEff As Double, Freqx As Double) As Double AnnEff_Effx = (1 + AnnEff) ^ (1 / Freqx) - 1 End Function What is the Logic that Allows Easy Choice and Naming of Function To use a function you need to be able to remember the name accurately. So naming, which we often relegate to a few seconds thought, is very important when there are 10 different functions for 10 different purposes. So I have derived and implemented a very simple algorithm for naming: 1. First I named the various rates and frequencies: Nomx and Nomy are Nominal (APR) rates compounded at the compounding frequencies per year of x and y. Effx and Effy are Effective rates for the frequencies of compounding per year of x and y Freqx and Freqy are required for arguments. They are the numeric values representing the number of compounding periods per year of Nomx and Nomy (two different Nominal (APR) rates). AnnEff is regarded as a special case, which indeed it is, because it is the only rate where the absulute level is the same for both Nominal and Effective. Nominal compounded 1 times per year *is* the annual effective rate. 2. This gives me my function name convention: RateYouHave_RateYouWant If there's only one species of Nominal rate (APR) or Effective rate then we use Nomx and Effx. Easy! I have Annual Effective. I want Nominal compounded monthly. Function name? AnnEff_Nomx I have a nominal rate compounded monthly (our common friend APR(12)) and I want the annual effective equivalent. Function name? Nomx_AnnEff What arguments are required and what order do they come in? 1. First argument is always the rate you have 2. Second argument is always freqx 3. If there is another frequency involved in the two rates (known + required) and if that frequency is not 1, then you need the third argument freqy. And that's all there is to it. With those formulas and functions you now have the base tools for a comprehensive range of calculations. A whole World of applications can now be developed. You are no longer constrained by simplifying assumptions that produce errors and distortions. And when you get results from Excel Functions and your applications, you can understand them and convert them to common bases for evaluation. For further and better explanations with examples including ones that integrate the functions in Excel financial functions see John Walkenbach's Excel 2002 Formulas. HTH -- Norman Harker Sydney, Australia Roll on Christmas 25th Dec and 7th Jan "DB." wrote in message ... | Here in UK, banks seeking depositors must (for comparison purposes) | quote the AER (Annual Equivalent Rate) for each type of account they | offer. So that although interest may be earned daily the AER tells us | what the accrued daily interest will total in a year's time. Thus | £2,000 invested on Jan.1st in an account offering 5.5% AER will have | £110 added a year later. | I wish to know what interest my deposit will have earned should I | close the account early. So: | In A1 I put the sum deposited. | In A2 I put the AER (as a percentage). | In A3 I put the number of days the money will have been in the account. | | What must I put in A4 to calculate the interest I might expect? | | TIA for any (all) reply (replies). As an old dog, slow at learning new | tricks, I regard you who answer our questions on this ng as geniuses! | | -- | DB. | | |
#6
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Interest calculations.
On Sat, 12 Apr 2008 19:24:44 GMT, "DB." wrote:
Here in UK, banks seeking depositors must (for comparison purposes) quote the AER (Annual Equivalent Rate) for each type of account they offer. So that although interest may be earned daily the AER tells us what the accrued daily interest will total in a year's time. Thus £2,000 invested on Jan.1st in an account offering 5.5% AER will have £110 added a year later. I wish to know what interest my deposit will have earned should I close the account early. So: In A1 I put the sum deposited. In A2 I put the AER (as a percentage). In A3 I put the number of days the money will have been in the account. What must I put in A4 to calculate the interest I might expect? TIA for any (all) reply (replies). As an old dog, slow at learning new tricks, I regard you who answer our questions on this ng as geniuses! Using Excel financial functions, and assuming 365 compounding periods per year, you could use this formula: =FV(NOMINAL(AER,365)/365,Days,,-Deposit) --ron |
#7
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Interest calculations.
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