Answer:
a) $11,940.52
b) $11,956.18
c) $11,966.81
d) $11,910.16
Explanation:
Given:
Investment amount = $10,000
Time = 3 years
Interest rate = 6%
Now,
Amount = [tex]P\times(1+\frac{r}{n})^{nt}[/tex]
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
Thus,
a) compounded semiannually
n = 2
[tex]Amount = \$10,000\times(1+\frac{0.06}{2})^{2\times3}[/tex]
Amount = $10000 × 1.03⁶
or
Amount = $11,940.52
b) compounded quarterly
n = 4
[tex]Amount = \$10,000\times(1+\frac{0.06}{4})^{4\times3}[/tex]
Amount = $10000 × 1.015¹²
or
Amount = $11,956.18
c) compounded monthly
n = 12
[tex]Amount = \$10,000\times(1+\frac{0.06}{12})^{12\times3}[/tex]
Amount = $10000 × 1.00536³⁶
or
Amount = $11,966.81
d) compounded continuously
n = 12
[tex]Amount = \$10,000\times(1+\frac{0.06}{1})^{1\times3}[/tex]
Amount = $10000 × 1.06³
or
Amount = $11,910.16
