# Compound Interest: 3 Equal Ann. Repayments, $3,000 Loan, 9% Rate • NosajW In summary, to borrow$3,000 from a bank at an interest rate of 9% compounded annually and make three equal annual repayments of $1,185.16, the interest and principal payments for each year are as follows: Year 1: Principal =$3,000, Interest = $270Year 2: Principal =$2,084.84, Interest = $187.64Year 3: Principal =$1,087.31, Interest = $97.86 NosajW You are about to borrow$3,000 from a bank at an interest rate of 9% compounded annually. You are required to make three equal annual repayments in the amount of $1,185.16 per year, with the first repayment occurring at the end of year one. For each year, show the interest payment and principal payment. I know how to do compound interest, but I don't get what this three equal annual repayments thing is. Can someone explain how to do this problem? Thanks in advance 3 payments/year means that a payment is made each 4 months of 1/3rd the annual payment? Last edited: it's not three payments a year. there's a total of three equal annual payments of$1,185.16. I'm supposed to find out the interest and principal per year

Oh I see
Well $3,000 is the principle. 9% of$3000 is interest. Subtract the payment from their sum. Then another 9% on this number for the 2nd year interest, etc.

Last edited:
it says three equal payments of 1185.16 but if you multiply that by 3 you don't get 3000(1.09)^3 = 3885.09 how would you do it annually instead of 3 years?

Crusty said:
Oh I see
Well $3,000 is the principle. 9% of$3000 is interest. Subtract the payment from their sum. Then another 9% on this number for the 2nd year interest, etc.

their sum is 1185.16*3?

Paying once a year, then adding interest on the remainder-
((3000*1.09-1185.16)*1.09-1185.16)*1.09-1185.16 = 0.014004 so there's some left over.

Last edited:
is there a formula for this? so..
year 1 = 3000*1.09 - 1185.16 = 2084.84, principal = 3000, interest = 270
year 2 = 2084.84*1.09 - 1185.16 = 1087.32, principal = 2084.84, interest = 187.64
year 3 = 1087.32*1.09 - 1185.16 = 0, principal = 1087.32, interest = 97.86

is this correct?

Assuming the interest is paid first and then the principle is paid down each year, then yes the new 9% each year would be all the interest.
If the fractions of pennies are kept by the loan giver or left off the equations, then there's nothing left at the end of year 3.

3000 * 1.09 - 1 185.16 = 2 084.84
2084.84 * 1.09 - 1 185.16 = 1087.3156; 1087.3156-.0056 = 1087.31
1087.31 * 1.09 - 1 185.16 = 0.0079; 0.0079-0.0079 = 0

you have been very helpful, thank you crusty!

## Related to Compound Interest: 3 Equal Ann. Repayments, $3,000 Loan, 9% Rate ## 1. What is compound interest? Compound interest is the interest calculated on the initial principal amount, as well as on the accumulated interest from previous periods. This results in a compounding effect and leads to a higher overall amount of interest earned. ## 2. How does compound interest work? Compound interest works by adding the interest earned to the principal amount, creating a new, higher principal amount for the next period's interest calculation. This process repeats until the loan or investment reaches maturity. ## 3. What are 3 equal ann. repayments? 3 equal ann. repayments refer to a loan repayment plan where the borrower agrees to pay back the loan in three equal annual payments. Each payment includes both the principal amount and the accrued interest. ## 4. How much is the$3,000 loan?

The $3,000 loan refers to the initial principal amount borrowed, which is$3,000.

## 5. What is the 9% rate in relation to compound interest?

The 9% rate represents the annual percentage rate (APR) of interest applied to the \$3,000 loan. This rate is used to calculate the interest earned on the loan over time.

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