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Claire has borrowed 5,000$. She plans to pay off the loan in full after two payments. She will make one payment 3 years from now, then another payment 6 years from now. The second payment will be exactly double the amount of the first payment. How much is the first payment if the interest rate of the loan is 8.5$, compounded annually? Express your answer as a dollar value rounded to the nearest cent.

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Answer:

The first repayment made after 3 years from the time of borrowing is : $2,489.05

Explanation:

Denote the valued needed to be found is x; which is the first repayment.

As the second repayment is double the amount of the first payment, 2x is the second repayment of Clarie on the borrowed amount.

The present value of the first payment discounted at the interest rate of the loan 8.5% compounded annually: x / 1.085^3

The present value of the second payment discounted at the interest rate of the loan 8.5% compounded annually: 2x/ 1.085^6

We have: (x/1.085^3) + (2x /1.085^6) = 5,000 <=> 2.0088 x = 5,000 <=> x = $2,489.05

So the first payment will be $2,489.05 and the second payment will be $4,978.10 ( 2x $2,489.05)

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