Answer:
$10,307.11
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
- A = Final amount.
- P = Principal amount.
- r = Interest rate (in decimal form).
- n = Number of times interest is applied per year.
- t = Time (in years).
Given:
- P = $8,200
- r = 5.8% = 0.058
- n = 2 (semi-annually)
- t = 4 years
Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=8200\left(1+\dfrac{0.058}{2}\right)^{2 \times 4}[/tex]
[tex]\implies \sf A=8200\left(1+0.029\right)^{8}[/tex]
[tex]\implies \sf A=8200\left(1.029\right)^{8}[/tex]
[tex]\implies \sf A=8200\left(1.25696445...\right)[/tex]
[tex]\implies \sf A=10307.10856...[/tex]
Therefore, the value of Sarah's investment after four years is $10,307.11 (nearest cent).
