The discount method is a method for computing interest on an installment loan. With the discount method, you calculate the interest based on a discount rate that is multiplied times the amount borrowed and by the number of years to repay the loan. The interest is then subtracted from the amount of the loan, and only the difference is given to the borrower. Thus, the interest is paid up front. For loans using the discount method, the monthly payment amount is calculated based on the entire loan amount, including the discounted interest. Consider the following example:

Deshi Chen from Boise, Idaho, borrows $3,500 (including interest) for three years (36 months) at an interest rate of 5% per year. The loan uses the discount method for determining the amount of interest.

Required:
a. How much of the loan amount ($3,500) consists of interest?
b. How much of the loan is actually given directly to Jack?
c. What is the monthly payment (rounded to the nearest penny), assuming 36 monthly payments?

a. The amount of the loan that is consist of interest is $525.

b. The amount of the loan that is actually given directly to Jack is $2,975.

c. The monthly payment (rounded to the nearest penny), assuming 36 monthly payments is $97.22.

Explanation:

a. How much of the loan amount ($3,500) consists of interest?

Interest = Discount rate * Amount borrowed * Number of years to repay the loan =

Where;

Discount rate = interest rate  = 5%

Amount borrowed = $3,500

Number of years to repay the loan = 3

Substituting the values into equation (1), we have:

Interest = 5% * $3,500 * 3

Interest = $525

Therefore, the amount of the loan that is consist of interest is $525.

b. How much of the loan is actually given directly to Jack?

Amount given to Jack = Amount borrowed - Interest = $3,500 - $525 = $2,975

Therefore, the amount of the loan that is actually given directly to Jack is $2,975.

c. What is the monthly payment (rounded to the nearest penny), assuming 36 monthly payments?

Monthly payment = Amount borrowed / Number of months = $3,500 / 36 = 97.2222222222222

Rounding to the nearest penny, we have:

Monthly payment = $97.22

Therefore, the monthly payment (rounded to the nearest penny), assuming 36 monthly payments is $97.22.

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