Answer:
r = 9.86%
Explanation:
The formula for calculating the future value of an invested amount yielding a compound interest is given by:
[tex]FV=PV(1+\frac{r}{n})^{nt}[/tex]
where:
FV = future value = $16,000
PV = present value = $10,000
r = interest rate = ?
n = number of compounding period per year = 1
t = time in years = 5
∴ [tex]16000=10000(1+\frac{r}{1})^{5}[/tex]
dividing both sides by 10,000
[tex]\frac{16000}{10000} =\frac{10000(1+\frac{r}{1})^{5}}{10000}[/tex]
[tex]1.6 = (1 + r)^{5}[/tex]
to remove the power of 5, we have to take the 5th root of both sides:
[tex](1.6)^{1/5} = (1 + r )^{5 * 1/5}[/tex]
Using your calculator:
1.09856 = 1 + r
∴ r = 1.09856 - 1 = 0.09856
r = 0.0986 = 9.86%
∴ r = 9.86%
