Suppose you make a down payment of 20% of $27,600 and finance the rest at 1.5% compounded monthly for 48 months. How much interest do you pay over the life of the loan? $ Round to the nearest dollar. tA
Suppose you make a down payment of 20% of $27,600 and finance the rest at 1.5% compounded monthly for 48 months. How much interest do you pay over the life of the loan? $ Round to the nearest dollar. tA
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Calculating Monthly Compounded Interest on a Loan**
**Problem Statement:**
Suppose you make a down payment of 20% of $27,600 and finance the rest at 1.5% compounded monthly for 48 months. How much interest do you pay over the life of the loan?
_$__________. Round to the nearest dollar._
**Explanation:**
This problem involves financial calculations related to loan payments and interest accumulation. To solve this, we can follow these steps:
1. **Calculate the Down Payment:**
20% of $27,600:
\[
0.20 \times 27600 = 5520
\]
2. **Determine the Amount to be Financed:**
Subtract the down payment from the total cost:
\[
27600 - 5520 = 22080
\]
3. **Calculate the Monthly Interest Rate:**
The annual interest rate is 1.5%, compounded monthly. Therefore, the monthly interest rate is:
\[
\frac{1.5\%}{12} = 0.00125
\]
4. **Determine the Number of Payments (n):**
The loan term is 48 months.
5. **Compute the Monthly Payment Using the Formula for an Annuity:**
The formula to calculate the monthly payment (P) for a loan is:
\[
P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}
\]
where:
- \( r \) is the monthly interest rate
- \( PV \) is the present value (loan amount)
- \( n \) is the number of payments
Substitute in the values:
\[
P = \frac{0.00125 \cdot 22080}{1 - (1 + 0.00125)^{-48}}
\]
6. **Calculate Total Payments Made:**
Multiply the monthly payment by the number of payments (48 months).
7. **Determine the Total Interest Paid:**
Subtract the financed amount from the total payments made.
By following these steps, you can determine how much interest is paid over the life of the loan. Be sure to round your final answer to the nearest dollar.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d929fa4-2fdc-40c7-801d-1fbf9b4298bd%2Fe7fe00b9-9099-4574-a427-297ffa2962bd%2Fq7wwnlf_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating Monthly Compounded Interest on a Loan**
**Problem Statement:**
Suppose you make a down payment of 20% of $27,600 and finance the rest at 1.5% compounded monthly for 48 months. How much interest do you pay over the life of the loan?
_$__________. Round to the nearest dollar._
**Explanation:**
This problem involves financial calculations related to loan payments and interest accumulation. To solve this, we can follow these steps:
1. **Calculate the Down Payment:**
20% of $27,600:
\[
0.20 \times 27600 = 5520
\]
2. **Determine the Amount to be Financed:**
Subtract the down payment from the total cost:
\[
27600 - 5520 = 22080
\]
3. **Calculate the Monthly Interest Rate:**
The annual interest rate is 1.5%, compounded monthly. Therefore, the monthly interest rate is:
\[
\frac{1.5\%}{12} = 0.00125
\]
4. **Determine the Number of Payments (n):**
The loan term is 48 months.
5. **Compute the Monthly Payment Using the Formula for an Annuity:**
The formula to calculate the monthly payment (P) for a loan is:
\[
P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}
\]
where:
- \( r \) is the monthly interest rate
- \( PV \) is the present value (loan amount)
- \( n \) is the number of payments
Substitute in the values:
\[
P = \frac{0.00125 \cdot 22080}{1 - (1 + 0.00125)^{-48}}
\]
6. **Calculate Total Payments Made:**
Multiply the monthly payment by the number of payments (48 months).
7. **Determine the Total Interest Paid:**
Subtract the financed amount from the total payments made.
By following these steps, you can determine how much interest is paid over the life of the loan. Be sure to round your final answer to the nearest dollar.
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