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:
Where:
- is the total amount you will pay to the lending company (Future Value).
- is the principal amount (the amount borrowed).
- is the annual interest rate (as a decimal).
- is the time period in years.
Now, substitute the values into the formula:
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:
- What is the total interest paid over the 33 years?
- How would the amount change if the interest rate were 9% instead of 11.27%?
- What if the loan term was reduced to 20 years—how much would you pay then?
- How does simple interest compare to compound interest in this situation?
- 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.
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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
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