Consider the following two loans for
P
0
=
$
10
,
000
.

Loan A:
5
-year loan, annual interest rate of
7
%
, monthly repayments of
$
198.01
.
Loan B:
3
-year loan, annual interest rate of
5
%
, monthly repayments of
$
299.71
.
On which loan will you pay the least interest?

Select the correct answer below:

Loan A

Loan B

To determine which loan results in paying the least interest, we need to calculate the total amount paid over the life of each loan and subtract the principal ($10,000) from that to find the total interest paid.

### Loan A (5-year loan at 7%):
- Monthly payment = $198.01
- Number of months = 5 years × 12 months = 60 months

The total amount paid over 60 months is:

\[
198.01 \times 60 = 11,880.60
\]

Interest paid on Loan A:

\[
11,880.60 - 10,000 = 1,880.60
\]

### Loan B (3-year loan at 5%):
- Monthly payment = $299.71
- Number of months = 3 years × 12 months = 36 months

The total amount paid over 36 months is:

\[
299.71 \times 36 = 10,789.56
\]

Interest paid on Loan B:

\[
10,789.56 - 10,000 = 789.56
\]

### Conclusion:
- Interest on Loan A: $1,880.60
- Interest on Loan B: $789.56

**Loan B** results in paying the least interest.

---

Do you need more details or have any questions?

Here are 5 related questions for further exploration:
1. How do different compounding periods affect loan interest?
2. How can you calculate the total interest paid on a loan with a variable interest rate?
3. What strategies can reduce the overall interest on a long-term loan?
4. How does loan amortization work for fixed-rate loans?
5. What is the impact of making extra payments on a loan's interest?

**Tip:** Always compare the total repayment amount when deciding between loans, as shorter-term loans typically result in less interest.

Consider the following two loans for P0 = $10,000. Loan A: 5-year loan, annual interest rate of 7%, monthly repayments of $198.01. Loan B: 3-year loan, annual interest rate of 5%, monthly repayments of $299.71. On which loan will you pay the least interest?

Learn how to compare two loans with different terms and interest rates to determine which results in paying the least interest. This problem involves key concepts of loan amortization, interest calculation, and total repayment analysis. Suitable for high school students and those interested in personal finance.

Math Problem Statement

Consider the following two loans for P 0

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation