Answer:
$3,559.25
Step-by-step explanation:
To find the amount owed after 4 years for a loan of $2,000 at an annual compound interest rate of 15.5%, we can use the compound interest formula.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$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 = $2,000
- r = 15.5% = 0.155
- n = 1 (annual)
- t = 4 years
Substitute the values into the formula and solve for A:
[tex]A=2000\left(1+\dfrac{0.155}{1}\right)^{1 \times 4}\\\\\\A=2000\left(1.155\right)^{4}\\\\\\A=2000(1.779622700625)\\\\\\A=3559.24540125\\\\\\A=\$3559.25\; \sf (nearest\;cent)[/tex]
Therefore, the amount owed after 4 years is:
[tex]\Large\boxed{\boxed{\$3559.25}}[/tex]
