Question

You borrow $2000 at 4% annual interest compounded quarterly, to be paid off with equal quarterly payments. Your first payment will be one year from now, and your last payment will be nine years from now. What will your payments be?

Answer 1

According to the information given in the above question it is seen that the Loan Amount of $4,000 is taken today at the rate of 4% per annum and compounded quaterly. But the repayments are to be made after year from now. and the period of the loan ends with the end of the 9th year from today.

hence, we are arrive at the following crucial information about the loan:

Loan Amount = $4,000

Rate of annual interest = 4%

but the compounding is done quaterly so we need to calculate quaterly interest rate which is 4% / 4 = 1% per quarter

Loan period = 9 years = 9 * 4 = 36 quarters.

Therefore, Total repayment amount for the loan = Principal amount * ( 1+ 1%)^loan period

Repayment Amount of the loan = $4,000 * (1+ 0.01)^36 = $5723.075

So, at the end of the loan period the amount that would be paid towards the loan will be equal to $5723.075

Now, equal quaterly payments = Total Loan Repayment Amount / Number of quaters until repayments

Number of quaters = Number of years * 4 = 8 * 4 = 32 quaters of repayment period.

Here we have taken Repayment period as 8 years because it is given in the question that the repayment will start after one year from today but will end at the end of nine years, hence the number of years till repayment (9-1 ) = 8 years.

Therefore, Quaterly Repayment amount = $5723.075 / 32 = $178.85 per quater.

Hence, Per Quater repayment amount is $178.85.