How long will it take to pay off a loan of 

​$53 comma 00053,000 

at an annual rate of 

77​% 

compounded monthly if you make monthly payments of 

​$400400 

​(round up)? 

Question content area bottom

Part 1

To pay off the​ loan, it will take approximately 

enter your response here 

years.  ​(Round up to the nearest​ integer.)

We can solve this problem using the formula for the number of months (n) required to pay off a loan with monthly payments, given a principal $ P $, an interest rate $ r $, and a monthly payment $ M $. The formula is:

\[
n = \frac{\log \left( \frac{M}{M - P \times r_{\text{monthly}}} \right)}{\log(1 + r_{\text{monthly}})}
\]

where:
- $ P = 53,000 $ is the loan amount,
- $ r_{\text{annual}} = 0.07 $ is the annual interest rate (7%),
- \( r_{\text{monthly}} = \frac{r_{\text{annual}}}{12} = \frac{0.07

How long will it take to pay off a loan of $53,000 at an annual rate of 7% compounded monthly if you make monthly payments of $400 (round up)?

Learn how to calculate the time needed to pay off a loan of $53,000 with an interest rate of 7% compounded monthly and $400 monthly payments. This problem covers key concepts such as compound interest, logarithmic calculations, and loan amortization. Suitable for advanced high school or college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation