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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.

 Sep 26, 2020
 #1
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p = payment at 3 years

    loan amount at 3 years = 5000 (1.085)^3 = 6386.4456

 

p = 1/2 (6386.4456 - p )(1.085)^3

2p / (1.085)^3 = 6386.4456 - p

p = $ 2489.05

 Sep 26, 2020
 #2
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PMT=5000 / (1*1.085^-3 + 2*(1.085^-6))

 

PMT = $2,489.05

 Sep 26, 2020
edited by Guest  Sep 26, 2020

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