Question

You borrow $12,000 for nine months at 15.4% per year. To discharge the debt, you make equal payments of 3 months, 6 months, and 9 months. What is the amount of each payment? Use a focal date of nine months from now. Draw an appropriate time diagram.

Answer 1

Annual interest rate = 15.4%

Quarterly rate = 15.4/4 = 3.85%

Lets assume, the quartley payment = Y

After every 3 month, he will pay the Y amount.

After 3 month the total amount will be = 12000*(1 + .0385)

Payment = Y

After the 3 month, the remaining amount will be = 12000*(1 + .0385) - Y

After 6 month, the total amount will be = {12000*(1+.0385) - Y}*(1+.0385)

After 6 month, payment will be = Y

the remaining amount = [{12000*(1+.0385)- Y}*(1+.0385)}] - Y

After 9 month, the amount will be = [[{12000*(1+.0385)- Y}*(1+.0385)}] - Y]* (1+0385)

After 9 month, final payment will be = Y

The remaining amount will be [[{12000*1.0385 - Y}*1.0385] - Y]*1.0385

which is equal to 0

The equation will be:

[{(12000*1.0385) - Y}*1.0385} - Y]*1.0385 - Y = 0

The only unknown term is Y.

After solving the equation, we get, Y = 4311.88