Answer:
The present value = $3,602.30
Explanation:
To calculate this, we will use the formula for calculating the future value for an amount invested, compounded semiannually at a certain interest rate. This is done as follows:
[tex]FV\ =\ PV(1+\frac{r}{n})^{(n\times t)}\\[/tex]
where:
FV = Future value = $4,500
PV = Present value = ??
r = interest rate = 4.5% = 4.5/100 = 0.045
n = number of compunding period per year = semiannually = 2
t = time = 5
[tex]4,500\ =\ PV(1+\frac{0.045}{2})^{(2\times 5)}\\\\4,500 = PV( 1+0.0225)^{10}\\4,500 = PV(1.0225)^{10}\\4,500 = PV (1.249203)\\Dividing\ both\ sides\ by\ 1.249203\ and\ making\ PV\ the\ subject\ of\ the\ formula\\\PV = \frac{4,500}{1.249203} \\PV= 3,602.297[/tex]
Therefore, the present value = $3,602.30
