Question

Use the​ add-on method for determining interest on a loan of ​$​,2540 with an annual rate of 6​% and a term of 4 years.​ Then, determine the annual interest rate during the last month of the loan.

Answer 1

The total interest on the loan is $609.60. The annual interest rate during the last month of the loan is 21.6%.

Step-by-step explanation:

To determine the interest on a loan using the add-on method, we need to multiply the loan amount by the interest rate and then multiply by the number of years. In this case, the loan amount is $2,540, the interest rate is 6%, and the term is 4 years.

Interest = Loan amount × Interest rate × Term

Interest = $2,540 × 0.06 × 4 = $609.60

So, the total interest on the loan is $609.60.

To determine the annual interest rate during the last month of the loan, we divide the interest for the last month by the remaining balance of the loan. Since the loan is for 4 years, there are 48 monthly payments. So, the interest for the last month is:

Last month interest = Total interest / Number of payments

Last month interest = $609.60 / 48 = $12.70

And the remaining balance of the loan is:

Remaining balance = Loan amount - Total payments made

Remaining balance = $2,540 - ($12.70 × 47) = $841.90

Therefore, the annual interest rate during the last month of the loan is:

Annual interest rate = Last month interest / Remaining balance × 12

Annual interest rate = $12.70 / $841.90 × 12 = 0.018 × 12 = 0.216 = 21.6%

Answer 2

Part A

The interest on the loan is $609.6

Part B

The interest amount on the last month is $12.7

Step-by-step explanation:

Part A

With the add-on interest method, the interest on the loan is added before the monthly payment is determined

The monthly payment, A = (P × I)/n

Where;

A = The amount payed monthly

P = The principal amount borrowed = $2,540

I = The interest on the loan = P × R × T

R = The interest on the loan = 6%

T = The duration of the loan = 4 years

n = The number of monthly payment = 4 × 12 = 48

Plugging in the variables to the simple interest formula, we get;

I = $2,540 × 6/100 × 4 = $609.6

The interest on the loan, I = $609.6

Part B

The monthly payment is therefore;

∴ A = ($2,540 + $609.6)/48 = $65.61
`\overline 6`

The amount payed as interest on the last month,
`I_m`, is given as follows;

$65.61
`\overline 6` - $2,540/48 = $12.7

The amount payed as interest on the last month = $12.7