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

10 %

APR (compounded 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

Mortgage Amount = Monthly Payment * [{1 - (1 + r)^-n} / r]

= $600 * [{1 - (1 + 0.10/12)^-(4*12)} / (0.10/12)]

= $600 * [0.3286 / 0.0083]

= $600 * 39.4282

= $23,656.90

So, now to find the number of years to pay off the loan with new monthly payment;

Mortgage Amount = Monthly Payment * [{1 - (1 + r)^-n} / r]

$23,656.90 = $850 * [{1 - (1 + 0.10/12)^-(n*12)} / (0.10/12)]

$23,656.90 / $850 = [{1 - (1.0083)^-(n*12)} / 0.0083]

27.8316 * 0.0083 = 1 - (1.0083)^-(n*12)

(1.0083)^-(n*12) = 1 - 0.2319

-(n*12)[log(1.0083)] = log(0.7681)

-(n*12)[0.0083] = -0.2639

n = -0.2639 / [-12*0.0083] = 2.65

So, it will take 2.65 years to payoff the loan.