Question

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

Answer 1

Answer:

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