Question

You have $50,000 in student loans. You set up a plan to repay this debt with monthly payments over the next 15 years (so 180 total payments). Your first payment will be in one month, and you believe with raises at work that each payment can be 0.2% higher than the previous one (so, for example, if your first payment is $100, your second month payment would be $100.20). If your monthly interest rate on this loan is 0.4%, what will your first payment in one month be?

Answer 1

CF = Cash flow in year 1

R = Monthly interest rate

G = growth rate

Present value = CF / r - g {[1 - (1 + g) / (1 +r)ⁿ]

50,000 = CF / 0.004 - 0.002 {[1 - (1 + 0.002) / (1 +0.004)¹⁸⁰]

50,000 = CF / 0.002 {1 - 0.698428}

50,000 = CF / 0.002 {0.301572}

165,797.8222 = CF / 0.002

CF = 331.60

First month payment will be $331.60