Question

You have an outstanding student loan with required payments of $600 per month for the next four years. The interest rate on the loan is 8% APR​ (monthly). Now that you realize your best investment is to prepay your student​ loan, you decide to prepay as much as you can each month. Looking at your​ budget, you can afford to pay an extra $250 a month in addition to your required monthly payments of $600​ or $850 in total each month. How long will it take you to pay off the​loan?

Answer 1

Given required monthly payments = $600

interest rate on loan = 8% = 0.08

t = 4 years

m = 12 months

By using the below formula and substituting above values,

MP = P* (r/m) / (1-(1+(r/m)^-(mt)))

where MP = monthly payments = 600

P = Principal amount = ?

600 = P * (0.08/12) / (1-(1+(0.08/12)^-(12*4)))

600 = P * (0.006667) / (1-(1+0.006667)^-(48))

600 = P * (0.006667) / (1-(1.006667)^(-48))

600 = P * (0.006667) / (1-0.7269)

600 = P * (0.006667)/ 0.2730

P = (600 *0.2730) / 0.006667

P = 24577.15

So the principal amount is 24577.15

and it takes 4 years to repay loan having 8% interest rate.

If I pay 850 monthly instead of 600, it takes me 24577.15/850 = 29 months for me to repay

or 29/12 = 2 years and 4 months for repaying he loan.