Answer:
$807.39
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
- P = $500
- r = 4% = 0.04
- n = 12 (monthly)
- t = 12 years
Substitute the given values into the compound interest formula and solve for A:
[tex]\implies A=500\left(1+\dfrac{0.04}{12}\right)^{12 \cdot 12}[/tex]
[tex]\implies A=500\left(1.00333333...\right)^{144}[/tex]
[tex]\implies A=500\left(1.61478492...\right)[/tex]
[tex]\implies A=807.392461...[/tex]
Therefore, Alyson will have $807.39 (nearest cent) in her account at the end of 12 years.
