## Related questions with answers

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. Discuss the pros and cons of each loan.

You need a $\$ 60,000$ loan.

$\quad$ Option $1$: a $30$-year loan at an $\mathrm{APR}$ of $7.15 \%$

$\quad$ Option $2$: a $15$-year loan at $6.75\%$

Solution

VerifiedThe **monthly payment** 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.

On the other hand, the **total amount paid over the term**, can be computed using the formula below.

$\text{total amount paid} = \text{PMT} \times \text{loan term in months}$

where $\text{PMT}$ is the regular payment amount and the loan term in months can be calculated by multiplying the loan term in years to $12$.

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