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 the 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 or borrowed for, in years.

In this problem:

• $P = 31000$
• $r = 8.5\% = 0.085$
• $n = 1$ (compounded annually)
• $t = 9$

Step2: Substitute the values into the formula

Substitute the values into the formula:
$A = 31000(1 + \frac{0.085}{1})^{1\times9}$
Simplify the expression inside the parentheses:
$1 + 0.085 = 1.085$
So the formula becomes:
$A = 31000(1.085)^{9}$

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

First, calculate $(1.085)^{9}$. Using a calculator, $(1.085)^{9}\approx1.085^9\approx2.07799$ (this value is obtained using a calculator for the exponentiation).

Step4: Calculate the amount $A$

Multiply the principal by the value obtained in Step3:
$A = 31000\times2.07799$
$A\approx31000\times2.07799 = 64417.69$

Step5: Round to the nearest dollar

Rounding $64417.69$ to the nearest dollar gives $64418$.

Answer:

$\$64418$