Question

A prize pays $16,000 each quarter for 3 years (12 payments)commencing in exactly 6 months’ time. If the appropriate discount rate is 10.0% p.a compounding quarterly, the value of the prize today is (round to nearest cent; don’t use $ sign or commas):

[HINT: the annuity is deferred]

Select one:

a. $160121.20

b. $164124.23

c. $2434800.44

d. $36172.39

Answer 1

Answer :

This can be solved using the Present value of annuity payments formula,

Present value of annuity = P * [ ( 1 - ( 1 + r ) ^ -n) / r ]

P is Quarterly payment = $ 16,000

r is Quarterly interest rate = ( 10% / 4 ) = 2.5%

n is no.of quarters = 3 * 4 = 12 quarters

Value of the prize today = Present value of annuity

Present value of annuity = 16,000 * [ ( 1 - ( 1 + 0.025 )^-12 ) / 0.025

Present value of annuity = 16,000 * ( 0.256444115 / 0.025 )

Present value of annuity = 16,000 * 10.2577646

Present value of annuity = $164,124.23

Value of the prize today is $ 164,124.23 i.e., option ( b )