Question

noah and adriana deposit $2,000.00 into a savings account which earns 13% interest compounded monthly. they want to use the money in the account to go on a trip in 2 years. how much will they be able to spend? use the formula $a = p\left(1 + \frac{r}{n}\
ight)^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Explanation:

Step1: Identify given values

$P = 2000$, $r = 0.13$, $n = 12$, $t = 2$

Step2: Calculate $\frac{r}{n}$

$\frac{0.13}{12} \approx 0.010833$

Step3: Calculate $1+\frac{r}{n}$

$1 + 0.010833 = 1.010833$

Step4: Calculate $nt$

$12 \times 2 = 24$

Step5: Calculate $(1+\frac{r}{n})^{nt}$

$1.010833^{24} \approx 1.293003$

Step6: Calculate final amount $A$

$A = 2000 \times 1.293003$

Answer:

$2586.01$