Question

A prize pays $16,000 each quarter for 4 years (16 payments)commencing in exactly 6 months’ time. If the appropriate discount rate is 9.7% 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]

Answer 1

The formula for Annuity is

here r is discount rate=0.097, n is number of times annuity is paid in the year=4, t is number of years the annuity will be paid=4 and C is the amount of annuity=$16,000

Substituting the values you will get=

Solving the equation further you will get=

Solving it further will give you= $210,104.39

This is the value of the prize from the date it will start, and according to the question the annuity will start 6 months after the present day (today) thus we will have to discount this to the present value.

The formula for PV for six months=

Thus putting this in the formula FV= $210,104.39, r= discount rate= (0.097)/2 as it is paid only for six months, t=time period=0.5

Substituting the value

Solving this will give you the Present value of the prize = $200,385.68