Question

A prize pays $16,000 each quarter for 5 years (20 payments)commencing in exactly 6 months’ time. If the appropriate discount rate is 5.9% 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. $63816.40 b. $275376.40 c. $271373.64 d. $4210853.69.

Answer 1

Let us first go through the given details in the question:

· Quarterly saving (investment)= $16000

· Discount rate =5.9% compounded quarterly

· Number of years =5 years*4 = 20 payments

· The quarterly saving will commence in 6 months time

Note:

· We can calculate the present value using either the IRR function of excel or TVM calculator/excel function.

The present value of the cash flow can be computed using excel or TVM calculator using the following inputs:

· PMT = 16000

· N=20

· I/Y=5.9/4 (as compounded quarterly)

· Compute PV = 275376.3969

Here, PMT= payment or investment per month, in this case, N=Number of years of investment, I/Y= Interest paid/received, PV=Present Value.

This 275376.3969$ will available after 6 months.

Answer is b

You can also calculate the value as on today. To find the value as on today following inputs can be used:

Note: We will use Effective annual rate formula: I = (1+r/m)^m−1

Here

I=effective interest rate(actual interest rate for a year)

r=Interest rate given (5.9%)

m=Number of compounding periods (Quarterly = 4)

Therefore, I=6.0318%

· FV=275376.3969

· N=0.5 years(6/12)

· I/Y=6.0318

· Compute PV = 267429.05

I hope you find the solution helpful.