The owner of the Blue Goose Motel borrowed $12 500 at 7.1% compounded semi-annually and agreed to repay the loan by making payments of $700 at the end of every three months.

(a)How many payments will be needed to repay the loan?

PV = 12500; PMT = 700; i = 7.1%/2 = 0.0355; c = 2/4 = 0.5

p = 1.0355 0.5 - 1 = 1.017595 - 1 = 0.017595

12500 = 700 (1 - 1.017595-n)

0.017595

17.86 = (1 - 1.017595-n)

0.017595

0.314247 = 1 - 1.017595-n

1.017595-n = 0.685753

-n 1n 1. 017595 = 1n 0.685753

Question: How do I calculate the next step in this question to solve for n and are my calculations correct up to this point?