K Use PMT= 1- P -nt to determine the regular payment amount, rounded to the nearest cent. The cost of a 1+ home is financed with a $100,000 40-year fixed-rate mortgage at 3%. a. Find the monthly payments and the total interest for the loan. b. Prepare a loan amortization schedule for the first three months of the mortgage. a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.) The total interest for the loan is $ (Use the answer from part a to find this answer. Round to the nearest cent as needed.) b. Fill out the loan amortization schedule for the first three months of the mortgage below. Payment Number Principal Loan Balance Interest QL D a H
K Use PMT= 1- P -nt to determine the regular payment amount, rounded to the nearest cent. The cost of a 1+ home is financed with a $100,000 40-year fixed-rate mortgage at 3%. a. Find the monthly payments and the total interest for the loan. b. Prepare a loan amortization schedule for the first three months of the mortgage. a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.) The total interest for the loan is $ (Use the answer from part a to find this answer. Round to the nearest cent as needed.) b. Fill out the loan amortization schedule for the first three months of the mortgage below. Payment Number Principal Loan Balance Interest QL D a H
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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Question
Answer both questions
![To determine the regular payment amount, rounded to the nearest cent, use the formula:
\[ \text{PMT} = \frac{P \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}} \]
The cost of a home is financed with a $100,000 40-year fixed-rate mortgage at 3%.
a. **Find the monthly payments and the total interest for the loan.**
b. **Prepare a loan amortization schedule for the first three months of the mortgage.**
---
a. **The monthly payment is $_____**
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total interest for the loan is $_____
(Use the answer from part a to find this answer. Round to the nearest cent as needed.)
b. **Fill out the loan amortization schedule for the first three months of the mortgage below.**
| Payment Number | Interest | Principal | Loan Balance |
|----------------|----------|-----------|--------------|
| | | | |
Note: Input values in the blanks after performing the necessary calculations using the provided formula and details.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6030cbbc-dba6-4cc4-b2c7-5d66af95ec0b%2Ffde53333-956a-40c0-a68b-36e4c3663036%2F9v6z2a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To determine the regular payment amount, rounded to the nearest cent, use the formula:
\[ \text{PMT} = \frac{P \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}} \]
The cost of a home is financed with a $100,000 40-year fixed-rate mortgage at 3%.
a. **Find the monthly payments and the total interest for the loan.**
b. **Prepare a loan amortization schedule for the first three months of the mortgage.**
---
a. **The monthly payment is $_____**
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total interest for the loan is $_____
(Use the answer from part a to find this answer. Round to the nearest cent as needed.)
b. **Fill out the loan amortization schedule for the first three months of the mortgage below.**
| Payment Number | Interest | Principal | Loan Balance |
|----------------|----------|-----------|--------------|
| | | | |
Note: Input values in the blanks after performing the necessary calculations using the provided formula and details.
![### Loan Payment Formula and Amortization Schedule
#### Loan Payment Calculation
To determine the regular payment amount for a fixed-rate mortgage, use the following formula:
\[
\text{PMT} = P \left( \frac{r}{n} \right) \div \left[ 1 - \left( 1 + \frac{r}{n} \right)^{-nt} \right]
\]
Where:
- \( P \) = Principal loan amount
- \( r \) = Annual interest rate
- \( n \) = Number of payments per year
- \( t \) = Loan term in years
For this scenario, a home is financed with a $100,000 40-year fixed-rate mortgage at 3%.
**Tasks:**
a. Calculate the monthly payments and total interest for the loan.
b. Prepare a loan amortization schedule for the first three months.
#### Amortization Schedule
Complete the amortization schedule for the first three months of the mortgage below:
| Payment Number | Interest | Principal | Loan Balance |
|----------------|----------|-----------|--------------|
| 1 | $ | $ | $ |
| 2 | $ | $ | $ |
| 3 | $ | $ | $ |
*(Use the answer from part a to find these answers. Round to the nearest cent as needed.)*
This exercise will help you understand how your monthly payments affect both the interest and principal, as well as how the loan balance decreases over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6030cbbc-dba6-4cc4-b2c7-5d66af95ec0b%2Ffde53333-956a-40c0-a68b-36e4c3663036%2Fiv8echk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Loan Payment Formula and Amortization Schedule
#### Loan Payment Calculation
To determine the regular payment amount for a fixed-rate mortgage, use the following formula:
\[
\text{PMT} = P \left( \frac{r}{n} \right) \div \left[ 1 - \left( 1 + \frac{r}{n} \right)^{-nt} \right]
\]
Where:
- \( P \) = Principal loan amount
- \( r \) = Annual interest rate
- \( n \) = Number of payments per year
- \( t \) = Loan term in years
For this scenario, a home is financed with a $100,000 40-year fixed-rate mortgage at 3%.
**Tasks:**
a. Calculate the monthly payments and total interest for the loan.
b. Prepare a loan amortization schedule for the first three months.
#### Amortization Schedule
Complete the amortization schedule for the first three months of the mortgage below:
| Payment Number | Interest | Principal | Loan Balance |
|----------------|----------|-----------|--------------|
| 1 | $ | $ | $ |
| 2 | $ | $ | $ |
| 3 | $ | $ | $ |
*(Use the answer from part a to find these answers. Round to the nearest cent as needed.)*
This exercise will help you understand how your monthly payments affect both the interest and principal, as well as how the loan balance decreases over time.
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