Question

Seth, Janice, and Lori each borrow 5,000 for five years at an annual nominal interest rate of 12%, compounded semi-annually. Seth has interest accumulated over the five years and pays all the interest and principal in a lump sum at the end of five years. Janice pays interest at the end of every six-month period as it accrues and the principal at the end of five years. Lori repays her loan with 10 level payments at the end of every six-month period. Calculate the total amount of interest paid on all three loans.

Answer 1

Answer:

$3000 for Seth, $6000 for Janice and $6214.61 for Lori.

Explanation:

The formula that is used to calculate interest is $I = Prt$ where r is the interest rate, P is the principal amount of money and t is the time which is 6 months in the question since it is compounded semi-annually which means twice a year.

It is stated that Seth pays all the interest and the principal together at the end of the five year period so we need to calculate the total interest over the 5 years which is equal to 10 6-month periods. When we insert the numbers into the formula where r is 0.12, the I is calculated as $8000 which is the total amount that Seth has to pay.

It is stated that Janice pays the interest semi-annually at the end of every 6 month period and she pays the principal at the end of the 5 year period. When we calculate the interests paid for each period which is always 600, the total amount of interest paid comes up to $6000 and with the principal sum, the total amount paid is $11000.

It is stated that Lori pays her loan with 10 level payments at the end of each 6 month period. If we calculate the interest rate for each period and then take %10 of that amount which is the amount that is paid for that period. Then if we subtract the paid amount from the total, we can calculate the interest for the next period and find the amount paid for that period by taking 10% of the result.

Adding the sum paid for each period, she pays a total of $5805.92 at the end of the 5 years and she has $5408.69 left to pay at the end which together comes up to $11214.61 for Lori.

I hope this answer helps.

Answer 2

Answer:

The total amount of interest paid on all three loans is 8,748.

Explanation:

Each person has borrowed 5,000 for the same period and with the same interest rate. However, the repayment is made differently by each person.

We calculate the interest paid by each person, and then sum up the three interest payments.

Seth pays = [5000 x (1 + 0.12/2)^10] - 5000 = 3,954

Janice pays = 5,000 X 0.06 x 10 = 3,000

Lori pays = [(5,000 x 10) / 7.36] - 5,000 = 1,794

Total interest payment = 3,954 + 3,000 + 1,794 = 8,748