Math Problem Statement

An online lending company is offering simple interest personal loans based on consumer credit scores. With your credit score, you can borrow $2900$⁢2900 for 33 years at an interest rate of 11.27%11.27%. How much money will you pay the lending company at the end of 33 years? Round your answer to the nearest cent, if necessary.

Formulas

Simple Interest

I=PrtI=Prt

Future Value for Simple Interest

A=P(1+rt)A=P(1+rt)

Future Value for Compound Interest

A=P(1+rn)ntA=P(1+rn)nt

Future Value for Continuous Compound Interest

A=PertA=Pert

Annual Percentage Yield (APY)

APY=(1+rn)n−1APY=(1+rn)n−1

Solution

To solve the problem using simple interest, we will use the Future Value for Simple Interest formula:

A=P(1+rt)A = P(1 + rt)

Where:

  • AA is the total amount you will pay to the lending company (Future Value).
  • P=2900P = 2900 is the principal amount (the amount borrowed).
  • r=11.27%=0.1127r = 11.27\% = 0.1127 is the annual interest rate (as a decimal).
  • t=33t = 33 is the time period in years.

Now, substitute the values into the formula:

A=2900(1+0.1127×33)A = 2900(1 + 0.1127 \times 33)

Let's calculate the total amount you will pay at the end of 33 years.The total amount you will pay to the lending company at the end of 33 years is approximately $13,685.39.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the total interest paid over the 33 years?
  2. How would the amount change if the interest rate were 9% instead of 11.27%?
  3. What if the loan term was reduced to 20 years—how much would you pay then?
  4. How does simple interest compare to compound interest in this situation?
  5. What happens if you repay the loan early, say after 10 years?

Tip: When dealing with simple interest loans, the interest amount remains the same regardless of when you pay during the loan term.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Simple Interest
Future Value

Formulas

Simple Interest Formula: I = P * r * t
Future Value for Simple Interest: A = P(1 + r * t)

Theorems

-

Suitable Grade Level

Grades 9-12