Answer:
The answer is $86,167.57 (to 2 decimal places)
Explanation:
In this question, we are to calculate the present value of a certain amount that is compounded semiannually, and after 10 years, yields a future value of $200,000. To calculate this, we will use the formula for calculating present value as follows:
PV = FV ÷ [tex](1+\frac{r}{n})^{n*t}[/tex]
where:
PV = present value = ???
FV = future value = $200,000
r = interest rate in decimal = 8.6% = 0.086
n = compounding period pr year = semiannually = 2
t = time of compounding in years = 10
Therefore,
PV = 200,000 ÷ [tex](1+\frac{0.086}{2})^{2*10}[/tex]
PV = 200,000 ÷ [tex](1.043)^{20}[/tex] = $86,167.57
