Walter borrows $10,000 from his mother. He will repay her $2,000 at the end of each of the next four years and the balance at the end of the fifth year. If the interest rate is 12%, what is the amount to be paid at the end of the fifth year?

Question

Quizplus · Accepted Answer

To find the balance at the end of the fifth year, we need to find the present value of the four $2,000 payments that Walter will make. We can use the formula for the present value of an annuity to do this:

PV = PMT x [1 - (1 + r)^-n] / r

Where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

In this case, Walter will make four payments of $2,000 each, so PMT = $2,000, r = 12% / 4 = 3%, and n = 4. Plugging these values into the formula, we get:

PV = $2,000 x [1 - (1 + 0.03)^-4] / 0.03
PV = $6,924.16

So the balance at the end of the fifth year will be the present value of this amount plus the original $10,000 loan. Using the present value formula again with PMT = 0 (since there are no payments at the end), r = 12%, and n = 5, we get:

Balance = $6,924.16 x (1 + 0.12)^5 + $10,000
Balance = $14,795.65

Therefore, the answer is B) $6,924.16.

Walter Borrows $10,000 from His Mother