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Question

Suppose you have a student loan of $30,000\$ 30,000 with an APR\mathrm{APR} of 9%9 \% for 2020 years.

a. What are your required monthly payments?

b. Suppose you would like to pay the loan off in 1010 years instead of 2020. What monthly payments will you need to make?

c. Compare the total amounts you'll pay over the loan term if you pay the loan off in 2020 years versus 1010 years.

Solution

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Answered 1 year ago
Answered 1 year ago
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a.\bold{a.} The monthly payments can be calculated using the formula

PMT=P×(APRn)[1(1+APRn)(nY)]\text{PMT} = \dfrac{P \times \left( \dfrac{\text{APR}}{n} \right)}{\left[ 1 - \left(1 + \dfrac{\text{APR}}{n} \right)^{(-nY)} \right] }

where PMT\text{PMT} is the regular payment amount, APR\text{APR} is the annual percentage rate in decimal form, PP is the amount borrowed, nn is the number of payment periods per year, and YY is the loan term in years.


We compute for the monthly payments PMTPMT for a loan with the following conditions:

  • P=$30,000P = \$30,000
  • APR=9%APR = 9\%
  • Y=20Y = 20

Substituting these values, we have

PMT=$30,000×(0.0912)[1(1+0.0912)(12×20)]=$2250.8335872=$269.92\begin{aligned} PMT &=\dfrac{\text{\$30,000} \times \left( \dfrac{\text{0.09}}{12} \right)}{\left[1-\left(1 + \dfrac{\text{0.09}}{12} \right)^{(-12 \times 20)}\right] } \\ \\ &= \dfrac{\$225}{0.8335872} \\ \\ &= \textcolor{#4257b2}{\$269.92} \end{aligned}


The monthly payments would be $269.92\textcolor{#4257b2}{\$269.92} for the student loan.

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