Question
Suppose that a loan of \( \$ 5500 \) is given at an interest rate of \( 7 \% \) compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding. (a) Find the amount owed at the end of 1 year. \( \$ \square \) (b) Find the amount owed at the end of 2 years. \( \$ \square \)
Ask by Morrison Frank. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
(a) \$5885
(b) \$6296.95
Solution
Let's calculate the amount owed on the loan using the compound interest formula:
\[
A = P \times (1 + r)^n
\]
where:
- \( A \) = amount owed after \( n \) years
- \( P \) = principal amount (\$5,500)
- \( r \) = annual interest rate (7% or 0.07)
- \( n \) = number of years
### (a) Amount owed at the end of 1 year
\[
A = 5500 \times (1 + 0.07)^1 = 5500 \times 1.07 = \$5,885
\]
### (b) Amount owed at the end of 2 years
\[
A = 5500 \times (1 + 0.07)^2 = 5500 \times 1.1449 = \$6,296.95
\]
**Answers:**
(a) $5885
(b) $6296.95
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the amount owed at the end of each year with compound interest, you can use the formula: \[ A = P(1 + r)^t \] where \( A \) is the amount owed, \( P \) is the principal (the initial loan amount), \( r \) is the annual interest rate (expressed as a decimal), and \( t \) is the number of years. (a) For the end of 1 year: \[ A = 5500(1 + 0.07)^1 = 5500(1.07) = 5885 \] So, the amount owed at the end of 1 year is \( \$5885 \). (b) For the end of 2 years: \[ A = 5500(1 + 0.07)^2 = 5500(1.07)^2 = 5500(1.1449) \approx 6287.45 \] So, the amount owed at the end of 2 years is approximately \( \$6287.45 \).
