Question

Suppose the interest rate is 9% APR with monthly compounding. Then the present value of an annuity that pays $233 every quarter for the next seven years is closest to: Select one: a. $4791 b. $4744 c. $5041 d. $480

Answer 1

There are 12 moonths in a year

There are 4 quarters in a year

(1 + APR/n)^n - 1 = (1 + APR /n)^n - 1

(1 + 0.09/12)^12 - 1 = (1 + APR/4)^4 - 1

(1 + 0.0075)^12 - 1 = (1 + APR/4)^4 - 1

1.093807 - 1 = (1 + APR/4)^4 - 1

1.093807 = (1 + APR/4)^4

1.022669 = (1 + APR/4)

0.090676 or 9.0676% = APR

Quarterly rate = 9.0676% / 4 = 2.2669%

Number of periods = 7 * 4 = 28

Present value = Payments * [1 - 1 / (1 + r)^n] / r

Present value = 233 * [1 - 1 / (1 + 0.022669)^28] / 0.022669

Present value = 233 * [1 - 0.533848] / 0.022669

Present value = 233 * 20.563422

Present value = $4791