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Chapter 13: Problem 70

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to solve each problem. How much will Anna owe at the end of 4 yr if she borrows \(\$ 5000\) at a rate of \(7.2 \%\) compounded weekly?

Short Answer

Expert verified
Anna will owe approximately \$6691.13 at the end of 4 years.

Step by step solution

01

Write down the given values

We are given: - Principal amount (P): $5000 - Annual interest rate (r): \(7.2 \%\) - Number of times interest is compounded per year (n): weekly, that is 52 times a year - Number of years (t): 4 years
02

Convert the percentage interest rate to a decimal

We need to convert the interest rate from a percentage to a decimal value. To do this, divide the percentage by 100: \[r = \frac{7.2}{100} = 0.072\]
03

Substitute the given values into the compound interest formula

Now, we can substitute all the given values into the compound interest formula: \[A = 5000(1 + \frac{0.072}{52})^{(52)(4)}\]
04

Evaluate the expression inside the parentheses

Evaluate the expression inside the parentheses: \[(1 + \frac{0.072}{52}) = 1 + \frac{0.072}{52} = 1.001384615\]
05

Raise the result to the power of (52 * 4)

Now, raise the result in step 4 to the power of (52 * 4): \[(1.001384615)^{(52)(4)} = 1.3382256\]
06

Multiply the result by the principal amount

Finally, multiply the result in step 5 by the principal amount ($5000): \[A = 5000 \times 1.3382256 = 6691.128\]
07

Round the result to the nearest cent

To find the final amount Anna will owe, round the result to the nearest cent: \[A \approx \$6691.13\] At the end of 4 years, Anna will owe approximately $6691.13.

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