Repayments Question (1 Viewer)

[coyazayo]

Pat borrows $30 000 at 9% per annum reducible interest, calculated monthly. The loan is to be repaid in 60 equal monthly instalments.

Q. With the twelfth repayment, Pat pays an additional $5000,so this payment is $5622.75. After this, repayments continue at $622.75 per month. How many more repayments will be needed?

 

[Dettol]

One way to do it is find the amount owing after 11 repayments, each being 622.75 each (let this amount be P(11). Then for the twelve month, compound P(11) then subtract 5622.75. This amount, say Q is the amount after the twelve month. Now you can reset the timeline to t=0. Then repeat the process. So let P(1) be the amount after one more repayment, which is Q x 1.0075 - 622.75, and so on. Then find an expression for P(n), set P(n) =0, and solve for n.