Compound Interest: 3 Equal Ann. Repayments, $3,000 Loan, 9% Rate

[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

 

[Crusty]

3 payments/year means that a payment is made each 4 months of 1/3rd the annual payment?

 

[NosajW]

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

 

[Crusty]

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.

 

[NosajW]

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?

 

[NosajW]

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?

 

[Crusty]

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.

 

[NosajW]

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?

 

[Crusty]

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

 

[NosajW]

you have been very helpful, thank you crusty!