Question

an amount of $31,000 is borrowed for 9 years at 8.5% interest, compounded annually. assuming that no payments are made, find the amount owed after 9 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:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

In this problem, $P = 31000$, $r = 8.5\% = 0.085$, $n = 1$ (compounded annually), and $t = 9$.

Step2: Substitute values into the formula

Substitute the given values into the formula:
$A = 31000(1 + \frac{0.085}{1})^{1\times9}$

Simplify the expression inside the parentheses first: $1 + 0.085 = 1.085$

Then calculate the exponent: $1\times9 = 9$

So the formula becomes $A = 31000\times(1.085)^{9}$

Step3: Calculate $(1.085)^{9}$

Using a calculator, $(1.085)^{9} \approx 2.097941$

Step4: Calculate the amount $A$

Multiply the principal by the calculated value:
$A = 31000\times2.097941 \approx 31000\times2.097941$

$31000\times2.097941 = 31000\times2 + 31000\times0.097941 = 62000 + 3036.171 = 65036.171$

Rounding to the nearest dollar, we get $A \approx 65036$

Answer:

$\$65036$