Question

Today you borrow $13,500 to pay for your expected college costs over the next 4 years, including a master’s degree. 2 years from now, you determine that you need an additional $3,200 so you borrow this additional amount. Starting 4 years from the original loan (2 years from the 2nd loan), you begin to repay your combined debt by making annual payments of $2,900. You will make these payments for 10 years. Both loans earn an interest of 5.4% compounded quarterly.

1. Draw a cash flow diagram of this situation from your perspective.
2. What is the total value of your loans when you start to pay them off?

Answer 1

Refer the attached graph for the CFD

b. You start paying loan from the 4th year.

Interest rate = 5.4% compounded quarterly

Effective rate = (1 + 0.054/4)^4 -1 = 0.0551

Interest rate = 5.51% per year.

FV of loan amount

F = 13,500(F/P,5.51%,4) + 3,200(F/P,5.51%,2)

=> F = 13,500 × 1.0551^4 + 3,200 × 1.0551^2

=> F = 16,730.69 + 3,562.38

=> F = $ 20,293.07

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