Question

You borrow $15,000 for your tuition costs. You agree to make payments at the end of each month for the next 10 years. If the interest rate on this loan is 6%, how much is your monthly payment? How much do you still owe after 20 payments?

Answer 1

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Loan Amount = PV = $15,000

n = 10 *12 = 120 months

r = monthly interest rate = 6%/12 = 0.5%

Monthly loan payment = [r*PV] / [1 - (1+r)^-n]

= [0.5%*$15,000] / [1 - (1+0.5%)^-120]

= $75 / 0.450367267

= $166.530753

Therefore, Monthly loan payment is $166.53

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x = payments made = 20

P = monthly loan payment = $166.53

Remaining loan amounr = P * [ 1- (1+r)^-(n-x)] / r

= $166.53 * [1 - (1+0.5%)^-(120-20)] / 0.5%

= $166.53 * 0.392713224 / 0.005

= $13,079.7066

Therefore, remaining loan amount after 20 payments is $13,079.71