A certain college graduate Sallie Evans has 24000 in student

A certain college graduate, Sallie Evans, has $24,000 in student - loan debt at the end of her college career. The interest rate on this debt is 0.75% per month. If monthly payments on this loan are $432.61, how many months will it take for Sallie to repay the entire loan?

Solution

For annuity immediates,

Present value = C (1 - (1+i)^-n)/i

24000 = 432.61 (1 - (1+0.0075)^-n)/0.0075

24000 = 432.61 (1 - (1+0.0075)^-n)/0.0075

0.416079148 = 1 - (1+0.0075)^-n

(1+0.0075)^-n = 0.583920852

(1.0075)^-n = 0.583920852

Thus,

n = -log(0.583920852)/log(1.0075)

n = 72 [ANSWER]