Answer:
$2191.12
Step-by-step explanation:
We are asked to find the value of a bond after 10 years, if you invest $1000 in a savings bond that pays 4% interest, compounded semi-annually.
[tex]FV=C_0\times (1+r)^n[/tex], where,
[tex]C_0=\text{Initial amount}[/tex],
r = Rate of return in decimal form.
n = Number of periods.
Since interest is compounded semi-annually, so 'n' will be 2 times 10 that is 20.
[tex]4\%=\frac{4}{100}=0.04[/tex]
[tex]FV=\$1,000\times (1+0.04)^{20}[/tex]
[tex]FV=\$1,000\times (1.04)^{20}[/tex]
[tex]FV=\$1,000\times 2.1911231430334194[/tex]
[tex]FV=\$2191.1231430334194[/tex]
[tex]FV\approx \$2191.12[/tex]
Therefore, the bond would be $2191.12 worth in 10 years.
