Miller borrows $300,000 to be paid off in three years.The loan payments are semiannual with the first payment due in six months,and interest is at 6%.What is the amount of each payment?
A)$55,379.
B)$106,059.
C)$30,138.
D)$60,276.

Question

Quizplus · Accepted Answer

The correct answer is A because the amount of each payment is $55,379. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the annuityPMT is the amount of each paymentr is the interest rate per periodn is the number of periodsIn this case, the present value of the annuity is $300,000, the interest rate per period is 3% (since the interest rate is 6% per year and the payments are semiannual), and the number of periods is 6 (since there are 3 years and 2 payments per year). Plugging these values into the formula, we get:$300,000 = PMT * [1 - (1 + 0.03)^-6] / 0.03$300,000 = PMT * [1 - 0.80583] / 0.03$300,000 = PMT * 6.5514PMT = $300,000 / 6.5514PMT = $55,379

Miller Borrows $300,000 to Be Paid Off in Three Years