Suppose you take out a mortgage for $170000 at 3.12% interest, compounded monthly, for 15 years. Find the monthly payment, rounded to the nearest cent. Fill in the following amoritzation table, rounding to the nearest cent.
Suppose you take out a mortgage for $170000 at 3.12% interest, compounded monthly, for 15 years. Find the monthly payment, rounded to the nearest cent. Fill in the following amoritzation table, rounding to the nearest cent.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![### Mortgage Amortization Calculation
#### Problem Statement
Suppose you take out a mortgage for $170,000 at 3.12% interest, compounded monthly, for 15 years.
1. **Find the monthly payment**, rounded to the nearest cent.
2. **Fill in the following amortization table**, rounding to the nearest cent.
| Month | Interest Amount | Principle | Loan Balance |
|-------|------------------|-----------|----------------------|
| 0 | | | $170,000 |
| 1 | | | |
| 2 | | | |
| 3 | | | |
#### Instructions
1. To calculate the monthly payment, use the formula for the monthly mortgage payment:
\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- \(M\) is the monthly payment.
- \(P\) is the loan principal amount ($170,000).
- \(r\) is the monthly interest rate (annual rate/12).
- \(n\) is the number of payments (loan term in years × 12).
2. Fill in the amortization schedule:
- For each month, compute the interest amount, which is the remaining balance multiplied by the monthly interest rate.
- Subtract the interest amount from the monthly payment to get the principal amount paid.
- Subtract the principal amount paid from the remaining loan balance to get the new loan balance.
3. **Interactive Feature**: After filling each cell in the table, click "Check Answer" to verify your calculations.
This educational page helps students and learners understand how mortgage amortization works, allowing them to practice calculation of monthly payments and the distribution between interest and principal over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2F3014a026-a25c-4391-899e-3bec39a601da%2Fomwfueb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Mortgage Amortization Calculation
#### Problem Statement
Suppose you take out a mortgage for $170,000 at 3.12% interest, compounded monthly, for 15 years.
1. **Find the monthly payment**, rounded to the nearest cent.
2. **Fill in the following amortization table**, rounding to the nearest cent.
| Month | Interest Amount | Principle | Loan Balance |
|-------|------------------|-----------|----------------------|
| 0 | | | $170,000 |
| 1 | | | |
| 2 | | | |
| 3 | | | |
#### Instructions
1. To calculate the monthly payment, use the formula for the monthly mortgage payment:
\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- \(M\) is the monthly payment.
- \(P\) is the loan principal amount ($170,000).
- \(r\) is the monthly interest rate (annual rate/12).
- \(n\) is the number of payments (loan term in years × 12).
2. Fill in the amortization schedule:
- For each month, compute the interest amount, which is the remaining balance multiplied by the monthly interest rate.
- Subtract the interest amount from the monthly payment to get the principal amount paid.
- Subtract the principal amount paid from the remaining loan balance to get the new loan balance.
3. **Interactive Feature**: After filling each cell in the table, click "Check Answer" to verify your calculations.
This educational page helps students and learners understand how mortgage amortization works, allowing them to practice calculation of monthly payments and the distribution between interest and principal over time.
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