Drew receives an inheritance that pays him $50,000 every three months for the next two years. Which of the following is closest to the present value (PV) of this inheritance if the interest rate is 8.5% (EAR) ?

A) $400,000

B) $365,322

C) $364,309

D) $354,223

Option (C) $364,309

Explanation:

Data provided in the question:

Amount paid every 3 months, A = $50,000

Number of years = 2

Interest rate = 8.5% = 0.085

Now,

since amount is paid every 3 months therefore compounding will be done every quarter

thus,

total number of periods in 2 years, n = 4 * 2 = 8

Interest rate per period, r = 0.085 : 4 = 0.02125

Present value = A * [ 1 - (1 : (1 + r) ⁿ) ] : r

thus,

Present value = $50,000 * [ 1 - (1 : (1 + 0.02125) ⁸) ] : (0.02125)

or

= $50,000 * [ 0.1548 ] : (0.02125)

= $364,308.76 ≈ $364,309

Hence,

Option (C) $364,309