This is probably so easy it is frightening...

[Jethro]

....that l don't know the answer.

Ok some one borrows a principle of 10,000 at 10% compound interest. Their first payment is 500, hence the balance after the first payment would be 10,000 + (0.10 * 12) - 500.

OK so far so easy. The problem l am having is expressing the formula in a procedure, so that l can show payments and remaining principle over 1 year, 2 years etc.

Some one stop me from hitting my head against my desk.

[kedaman]

10000*1.1^years-sumof(n=1 to years-1,500*1.1^n)

[jim mcnamara]

Kedaman: 23 hours of daylight brings you to the forum nice and early... I had the same problem on a trip far North.

Jethro: This is called amortization. Search on
Planetsourcecode for 'amortize'

[HarryW]

I had to do this in an assignment for one of my modules a few months ago.. didn't know it had a name. That sum is a simple geometric series, so it can be simplified. I'll see if I can dig up the equations I came up with.

[HarryW]

Okay, this is my version:

R = 1 + i/12

P = ((1-R)RⁿC₀) / (1-Rⁿ)


Where P is the monthly payment, i is the annual interest rate, C₀ is the starting capital, n is the number of months after which there is no remaining capital.

This is for compounding monthly. If you want a different compound rate, you can change it around pretty easily.

[Guv]

This problem is poorly defined and there seems to be some confusion about terminology.

Apologies in advance for any typo’s in the following.

First, compound interest refers to interest on interest. The typical situations involving compound interest are savings accounts when there are no withdrawals and loans on which no payments are made. In these situations, the interest due is periodically added to the principal amount. Then, for each period, the interest percentage is applied to the total of the principal plus any previous interest amounts added to the principal. Assuming there are no payments on a loan or withdrawals/deposits from/to a saving account, the formula for compound interest is the following.

Amount = Principal * (1 + YearlyRate / 1200)^n

Where n is the number of months. This assumes a yearly interest rate applied monthly, which is common practice.

For your loan, it is customary to specify interest using a yearly rate, which is applied monthly. It is possible, but rare for the interest to be specified other than as a yearly rate, and it is unusual for the interest period not to be a month (calculated as 1/12 of a year, even though no month happens to be exactly 1/12 of a year).

I assume that you are talking about a normal commercial loan or mortgage with 10% annual interest calculated monthly and a monthly payment of $500.00. Based on those assumptions, the calculations for each month are as follows.

• InterestPayment = Principal * 10 / 1200, rounded to the nearest penny.
• PrincipalPayment = 500 - InterestPayment
• NewBalance = Principal - PrincipalPayment, which becomes the principal on which interest is calculated next month.

A schedule for the first few months would be as follows.

Principal    InterestPayment   PrincipalPayment
 10,000.00        83.33             416.67
  9,583.33        79.86             420.14
  9,163.19        76.36             423.64
  8.739.55        72.83             427.17

The concepts implied by the above can be applied to do calculations using different rates, rules, et cetera.

[jim mcnamara]

Guv - unless GAAP in your locale is different from the US you have it wrong. (GAAP = Generally Accepted Accounting Principles). Not your math, your assumptions. By the way, most guys who are decent at match mess this one up.

I'll log into work and present an accepted version of this here later.
Generally, the majority of early payments go to interest, little to principle.

(it's VAX BASIC, but you will have no trouble reading it.)

[Guv]

Jim McNamara: A $500.00 payment per month on a $10,000.00 loan at 10% would pay the loan off in 22 months, which is the reason for the low interest and high principal payments. $96.50 would be the normal payment on $10,000.00 for 20 years at 10%, which would result in the interest versus principal ratio you are thinking about ($83.33 for interest and $13.17 for principal).

I do not think my assumptions are contrary to GAAP. It is the size of the payment specified by Jethro which is high for a mortgage payment on $10,000.00, but perhaps not out of line for a small commercial loan to cover some unexpected business expense.

I will be surprised if your VAX program comes up with anything much different from the above.

[Jethro]

Yeah Guv has pointed out the complexity involved in the calc. Interest can accrue on interest.

e.g

10,000 @ 10%

after first month

11,000 @ 10%

after second month

12,100 @ 10%

etc etc etc. Each payment ids predominatly only a cover of the interest accrued from the previous month, and a slight reduction in principle. This changes over the course of the loan.

No it is not Amortisation it is soley a loan repayment schedule.

Thanks Harry that helped.

Am still hitting my head on the desk over this one cause it looks so easy....