Answer:
The present value is = $7325.48
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
