Barach ObamaBarbara borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments.The actual end-of-year payment is

Question

Quizplus · Accepted Answer

The total amount to be repaid over 4 years can be found using the formula:
$4,500(1+0.12)^4 = $7,981.06
The annual payment can be found by dividing this total by 4:
$7,981.06/4 = $1,995.26
However, this is the amount that would be paid if the payments were equal and there was no interest. Since interest is compounded annually, the actual end-of-year payment will be higher. Using the formula for the future value of an annuity due, we can find the actual end-of-year payment:
P = ($1,995.26 x (1+0.12) - 1)/0.12
P = $1,482.14, which is closest to option C ($1,482)

Barach ObamaBarbara Borrows $4,500 at 12 Percent Annually Compounded Interest