**Problem Statement:**Barbara decides to buy a house for $450,000. She makes a down payment of $40,000 at the time of purchase, and the balance is financed at 6% compounded monthly, with monthly payments made over:a) 10 years b) 20 years c) 30 years Find her monthly payment in each case, if the first payment is due one month from today.**Explanation:**This problem involves calculating the monthly payments on a fixed-rate mortgage for different loan terms. The amount to be financed is the purchase price minus the down payment. The interest rate is compounded monthly.**Calculation:**1. Determine the loan amount: - Total price: $450,000 - Down payment: $40,000 - Loan amount = $450,000 - $40,000 = $410,0002. Interest rate and compounding: - Annual interest rate: 6% - Monthly interest rate: 6% / 12 = 0.5% = 0.005 (expressed as a decimal)3. Number of payments: - a) 10 years: 10 × 12 = 120 payments - b) 20 years: 20 × 12 = 240 payments - c) 30 years: 30 × 12 = 360 payments4. Formula for monthly payment (M): \[ M = \frac{P \times r}{1 - (1 + r)^{-n}} \] Where: - $ M $ is the monthly payment - $ P $ is the principal amount ($410,000) - $ r $ is the monthly interest rate (0.005) - $ n $ is the total number of paymentsBy applying these calculations for each scenario, you will find the monthly payment for 10, 20, and 30-year loan terms.

here we calculate the monthly payment of the given by following given below as

10. Barbara decides to buy a house for $450,000. She makes a down payment of $40,000 at the time of purchase, and the balance is financed at 6% compounded monthly, with monthly payments made over a) 10 years b) 20 years and c) 30 years. Find her monthly payment in each case, if the first payment is due one month from today.

10. Barbara decides to buy a house for $450,000. She makes a down payment of $40,000 at the time of purchase, and the balance is financed at 6% compounded monthly, with monthly payments made over a) 10 years b) 20 years and c) 30 years. Find her monthly payment in each case, if the first payment is due one month from today.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**Problem Statement:**

Barbara decides to buy a house for $450,000. She makes a down payment of $40,000 at the time of purchase, and the balance is financed at 6% compounded monthly, with monthly payments made over:

a) 10 years
b) 20 years
c) 30 years

Find her monthly payment in each case, if the first payment is due one month from today.

**Explanation:**

This problem involves calculating the monthly payments on a fixed-rate mortgage for different loan terms. The amount to be financed is the purchase price minus the down payment. The interest rate is compounded monthly.

**Calculation:**

1. Determine the loan amount:

- Total price: $450,000
- Down payment: $40,000
- Loan amount = $450,000 - $40,000 = $410,000

2. Interest rate and compounding:

- Annual interest rate: 6%
- Monthly interest rate: 6% / 12 = 0.5% = 0.005 (expressed as a decimal)

3. Number of payments:

- a) 10 years: 10 × 12 = 120 payments
- b) 20 years: 20 × 12 = 240 payments
- c) 30 years: 30 × 12 = 360 payments

4. Formula for monthly payment (M):

\[
M = \frac{P \times r}{1 - (1 + r)^{-n}}
\]

Where:
- $ M $ is the monthly payment
- $ P $ is the principal amount ($410,000)
- $ r $ is the monthly interest rate (0.005)
- $ n $ is the total number of payments

By applying these calculations for each scenario, you will find the monthly payment for 10, 20, and 30-year loan terms.

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