## Related questions with answers

Suppose you have a student loan of $\$ 30,000$ with an $\mathrm{APR}$ of $9 \%$ for $20$ years.

a. What are your required monthly payments?

b. Suppose you would like to pay the loan off in $10$ years instead of $20$. 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 $20$ years versus $10$ years.

Solution

Verified$\bold{a.}$ The **monthly payments** can be calculated using the formula

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

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

We compute for the **monthly payments** $PMT$ for a loan with the following conditions:

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

Substituting these values, we have

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

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

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Using and Understanding Mathematics: A Quantitative Reasoning Approach

6th Edition•ISBN: 9780321914620 (7 more)Jeffrey O. Bennett, William L. Briggs#### Financial Algebra: Advanced Algebra with Financial Applications

2nd Edition•ISBN: 9781337271790Richard Sgroi, Robert Gerver## More related questions

1/4

1/7