A bank is negotiating a loan. The loan can either be paid off as a lump sum of $100 000 at the end of five years, or as equal annual payments at the end of each of the next five years. If the interest rate on the loan is 10%, what annual payments should be made so that both forms of payment are equivalent?

Question

Quizplus · Accepted Answer

To find the equivalent annual payments, we need to find the present value of the lump sum payment and then use the present value of an annuity formula to find the equal annual payments.

Present value of lump sum payment:
PV = FV / (1 + r)^n
PV = 100 000 / (1 + 0.10)^5
PV = 100 000 / 1.61
PV = 62 112.15

Now we can use the present value of an annuity formula to find the equal annual payments:
PV = P * [1 - 1/(1+r)^n] / r
62 112.15 = P * [1 - 1/(1+0.10)^5] / 0.10
62 112.15 = P * [1 - 1/1.6105] / 0.10
62 112.15 = P * 3.7908
P = 62 112.15 / 3.7908
P = 16 380.19

Therefore, the best choice is C: $16,380.

A Bank Is Negotiating a Loan