Find the present value of an ordinary annuity of $1,400 payments each made semiannually over 8 years and earning interest at 12% per year compounded semi-annually.
A) $14,148.25
B) $6,954.70
C) $9,763.58
D) $3,365.99

Question

Find the present value of an ordinary annuity of $1,400 payments each made semiannually over 8 years and earning interest at 12% per year compounded semi-annually. ​
A) $14,148.25
B) $6,954.70
C) $9,763.58
D) $3,365.99

Quizplus · Accepted Answer

The correct answer is A because the present value of an ordinary annuity is the sum of the present values of each payment. The present value of each payment is the payment amount divided by (1 + r/n)^(nt), where r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, r = 12%, n = 2, and t = 8. So, the present value of each payment is $1,400 / (1 + 0.12/2)^(2*8) = $1,400 / (1.06)^16 = $1,400 / 2.7148 = $519.52. The present value of the annuity is the sum of the present values of each payment, which is $519.52 * 16 = $8,312.32.

Find the Present Value of an Ordinary Annuity of $1,400