The following loan is a simple interest amortized loan with monthly payments.

Question

$289,000, 10 3/4%, 35 years

(a) Find the monthly payment. (Give your answer to the nearest cent.)

(b) Find the total interest for the given simple interest amortized loan. (Give your answer to the nearest cent.)

Answer 1

To solve this problem, we need to calculate the monthly payment and the total interest paid for a simple interest amortized loan. Here's how we can do it:

Part (a): Monthly Payment Calculation

The formula for the monthly payment 𝑀M on a simple interest loan is given by:

𝑀=𝑃×𝑟×𝑛+𝑃𝑛M=nP×r×n+P​

Where:

1. 𝑃P is the principal amount (loan amount)
2. 𝑟r is the annual interest rate (as a decimal)
3. 𝑛n is the total number of payments

Given:

1. P = \289,000 $
2. Annual interest rate =10.75%=0.1075=10.75%=0.1075
3. Loan term =35=35 years, so the total number of payments 𝑛=35×12=420n=35×12=420 months

Plugging these values into the formula:

𝑀=289,000×0.1075×35+289,000420M=420289,000×0.1075×35+289,000​

Let's calculate this.

Part (b): Total Interest Calculation

The total interest 𝐼I paid over the life of the loan can be calculated by:

𝐼=𝑀×𝑛−𝑃I=M×n−P

Where:

1. 𝑀M is the monthly payment
2. 𝑛n is the total number of payments
3. 𝑃P is the principal amount

Once we have 𝑀M from part (a), we can use it to find 𝐼I.

(a) Monthly Payment: The monthly payment for the loan is approximately $3,277.05.

(b) Total Interest: The total interest paid over the life of the loan is approximately $1,087,362.50.