Question

an amount of $49,000 is borrowed for 5 years at 4% interest, compounded annually. assuming that no payments are made, find the amount owed after 5 years. use the calculator provided and round your answer to the nearest dollar.

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $P$ is the principal amount ($49,000$),
• $r$ is the annual interest rate (as a decimal, $0.04$),
• $n$ is the number of times interest is compounded per year (annually, so $n = 1$),
• $t$ is the number of years ($5$).

Step2: Substitute values into formula

Substitute $P = 49000$, $r = 0.04$, $n = 1$, $t = 5$ into the formula:
$A = 49000(1 + \frac{0.04}{1})^{1 \times 5}$
Simplify the exponent and the fraction:
$A = 49000(1 + 0.04)^{5}$
$A = 49000(1.04)^{5}$

Step3: Calculate $(1.04)^5$ and multiply by 49000

First, calculate $(1.04)^5$. Using a calculator, $(1.04)^5 \approx 1.2166529024$.
Then multiply by 49000:
$A \approx 49000 \times 1.2166529024$
$A \approx 59616.0022176$

Step4: Round to nearest dollar

Rounding $59616.0022176$ to the nearest dollar gives $59616$.

Answer:

$\$59616$