You borrow $10,000 to pay for your college tuition.The loan is amortized over a three-year period with an interest rate of 18%.What is your remaining balance at the end of year two?

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly payment using the formula for the amortization of a loan:

PMT = (P*r)/(1-(1+r)^-n)

Where PMT is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the total number of payments.

In this case, P = $10,000, r = 0.18/12 = 0.015, and n = 3*12 = 36.

PMT = (10000*0.015)/(1-(1+0.015)^-36) ≈ $366.52

After one year, you will have made 12 payments of $366.52, totaling $4,398.24.

We can calculate the remaining balance after the first year as follows:

Remaining Balance after Year 1 = P*(1+r)^(n-12) - (PMT/r)*((1+r)^(n-12)-1)

Remaining Balance after Year 1 = 10000*(1+0.015)^(36-12) - (366.52/0.015)*((1+0.015)^(36-12)-1)

Remaining Balance after Year 1 ≈ $6,796.24

To find the remaining balance after the second year, we need to subtract the payments made during the second year (another 12 payments of $366.52, totaling $4,398.24) from the remaining balance after the first year:

Remaining Balance after Year 2 = $6,796.24 - $4,398.24 = $2,398.00

Finally, we need to calculate the remaining balance at the end of the third year. We can use the same formula as for the first year, but with n = 12:

Remaining Balance after Year 3 = P*(1+r)^(n-12) - (PMT/r)*((1+r)^(n-12)-1)

Remaining Balance after Year 3 = 10000*(1+0.015)^(12-12) - (366.52/0.015)*((1+0.015)^(12-12)-1)

Remaining Balance after Year 3 ≈ $0

Therefore, the remaining balance at the end of year two is approximately $3,898 (Choice C).

You Borrow $10,000 to Pay for Your College Tuition