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Sagot :
a) The future value if the interest is compounded semiannually = $12432
b) The future value if the interest is compounded annually = $12389
The future value for compound interest is given as:
[tex]FV=P(1+\frac{r}{n})^{nt}[/tex]
The amount invested is the principal
The principal, P = $8704.56
The rate, r = 4% = 0.04
The interest is compounded semiannually
n = 2
Time, t = 9 years
Substitute these parameters into the equation above
[tex]FV=8704.56(1+\frac{0.04}{2})^{2(9)}\\\\FV=8704.56(1.02)^{18}\\\\FV=\$12432[/tex]
b) The future value if the interest is compounded annually
n = 1
[tex]FV=8704.56(1+\frac{0.04}{1})^{1(9)}\\\\FV=8704.56(1.04)^{9}\\\\FV=\$12432\\\\FV=\$12389[/tex]
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