Barach Obama borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments.The actual end-of-year payment is
A)$942
B)$1,125
C)$1,482
D)$2,641

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity,

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

where PV is the present value of the loan (which is borrowed), PMT is the end-of-year payment, r is the annual interest rate, and n is the number of payments.

Substituting the given values, we have:

$4,500 = PMT [(1 - (1 + 0.12)^-4) / 0.12]
$4,500 = PMT [3.037]

Therefore, the end-of-year payment (PMT) is:

PMT = $4,500 / 3.037
PMT = $1,482.29

Rounding to the nearest dollar gives us the actual end-of-year payment of $1,482, which is choice C.

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