Loan Repayments (1 Viewer)

[DJel]

"A $2000 loan is offered at 18% p.a. interest, charged monthly, over 4 years. If no repayments need to be paid for the first 3 months, find the amount of each repayment. How much will be paid back altogether?"

I can get close to the answer but the answer given is "$64.25; $2891.25"

Thanks for any help.

 

[sicmacao]

"A $2000 loan is offered at 18% p.a. interest, charged monthly, over 4 years. If no repayments need to be paid for the first 3 months, find the amount of each repayment. How much will be paid back altogether?"

I can get close to the answer but the answer given is "$64.25; $2891.25"

Thanks for any help.

Let An be the amount owing at the end of the nth month.
r = 1 + 18/12% = 101.5% = 1.015
Let M be the amount of the monthly repayment.

Then
A1 = 2000r
A2 = 2000r^2
A3 = 2000r^3
A4 = 2000r^4 - M
A5 = 2000r^5 - Mr - M
.
.
.
A48 = 2000r^48 - M(r^44 + r^43 + ... +1)
= 2000^48 - M(r^45-1)/(r-1) (sum of GP)
But the loan will be repaid after 4 years or 48 months so A48 = 0

solving for M we get

M = 2000r^48(r-1)/(r^45-1)
substituting r = 1.015 yields 64.2459.... rounding to $64.25
Total repayment is $64.25*45 = $2891.45 (since no repayment in the first 3 months)

 

[DJel]

Cool, thanks. I found my mistake, I wasn't adding interest for the first three months.