Question

An investment that you are considering promises to pay $2000 semiannually for the next two years, beginning six months from now. You have determined that the appropriate opportunity cost (discount rate is 8%, compounded quarterly. What is the value of this investment?

Answer 1

The present value is = $7325.48

Step-by-step explanation:

Step 1: Know the formula for the Present Value of the investment

PV formula = PMT x [1- (1/(1+ r)^n)] /r

Where PMT = Annuity Amount

r = Discount Rate

n= number of years or period

Step 2: fill in the necessary figures for the formula

PMT= $2000

Semi-annually = 2000/2 = 1000

r= 8%, however, compounded quarterly = 8/4 (quarter) = 2% per quarter

n= 2 years... however since it is to be compounded quarterly, 2 x 4(quarterly compounding) = 8

Therefore, Present Value =

The semi- annual PMT, the 2% quarterly rate, the 8 for number of years will be used

PV= 1000 x [1- (1/(1+ 0.02)^8] /0.02

= 1000 x 7.32548

The present value of the investment is = $7325.48