1 / 2

The Flemings secured a bank loan of $272,000 to help finance the purchase of a house. The bank charges interest at a rate of 5%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term? (Round your answer to the nearest cent.)

This problem involves calculating the monthly payment required to amortize a loan over a given period of time, using a fixed interest rate. We can solve it using the formula for the monthly payment of an amortizing loan, which is given by:

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

Where:
- $ M $ = monthly payment
- $ P $ = principal (loan amount)
- $ r $ = monthly interest rate (annual interest rate divided by 12)
- $ n $ = total number of payments (number of months)

### Given:
- Loan amount $ P = 272,000 $
- Annual interest rate = 5%, so the monthly interest rate $ r = \frac{5\%}{12} = \frac{0.05}{12} $
- Loan term = 25 years, which corresponds to $ n = 25 \times 12 = 300 $ months

Now, we can substitute these values into the formula.

\[
r = \frac{0.05}{12} = 0.00416667
\]

\[
n = 25 \times 12 = 300
\]

Now, substituting these into the formula for $ M $:

\[
M = 272,000 \times \frac{0.00416667(1+0.00416667)^{300}}{(1+0.00416667)^{300} - 1}
\]

Let's calculate this.The Flemings should make monthly payments of **$1,590.08** to fully amortize the loan over 25 years.

Would you like further details or clarifications on how this calculation works?

Here are five related questions:
1. How would the monthly payment change if the interest rate increased to 6%?
2. What would happen to the loan term if they made larger monthly payments?
3. How much total interest will they pay over the life of the loan?
4. Can the loan be paid off early, and how would this impact total interest?
5. How would the payment be affected if they chose a 30-year mortgage instead?

**Tip:** When you pay extra towards a loan's principal, you can reduce both the interest paid and the total repayment time!

The Flemings secured a bank loan of $272,000 to help finance the purchase of a house. The bank charges interest at a rate of 5%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term? (Round your answer to the nearest cent.)

Discover how to calculate the monthly payment for a $272,000 loan with a 5% annual interest rate, amortized over 25 years. This problem covers key financial mathematics concepts, including loan amortization and compound interest, with step-by-step calculations for a practical real-world scenario.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation