Question

aiden invested $5,700 in an account paying an interest rate of 5.7% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 17 years?

Explanation:

Step1: Recall compound interest formula

The formula for compound interest (compounded annually) is:
$$A = P(1 + r)^t$$
where $A$ is the final amount, $P$ is the principal, $r$ is the annual interest rate (decimal), and $t$ is time in years.

Step2: Convert rate to decimal

$$r = \frac{5.7}{100} = 0.057$$

Step3: Substitute values into formula

$P = 5700$, $r=0.057$, $t=17$:
$$A = 5700(1 + 0.057)^{17}$$

Step4: Calculate $(1.057)^{17}$

$$(1.057)^{17} \approx 2.5503$$

Step5: Compute final amount

$$A \approx 5700 \times 2.5503 = 14536.71$$

Step6: Round to nearest ten dollars

Round $14536.71$ to the nearest ten: $14540$

Answer:

$\$14,540$