Answer:
$595.69
Step-by-step explanation:
To determine how much David will have in his account after 4 years if he deposits $550 and it earns 2% interest compounded quarterly, we can use the compound interest formula.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
In this case:
- P = $550
- r = 2% = 0.02
- n = 4 (quarterly)
- t = 4 years
Substitute the values into the formula:
[tex]A=550\left(1+\dfrac{0.02}{4}\right)^{4 \times 4}[/tex]
Now, solve for A:
[tex]A=550\left(1+0.005\right)^{16}[/tex]
[tex]A=550\left(1.005\right)^{16}[/tex]
[tex]A=550\left(1.0830711512...\right)[/tex]
[tex]A=595.6891332...[/tex]
[tex]A=\$595.69[/tex]
Therefore, David will have $595.69 in his account in 4 years.
