Answer
a) $\$482.77$
b) $\$608.56$
Work Step by Step
a) The loan must be repaid with regular payments $R$, so the payments from an annuity whose present value $A_p$ represents the amount of the loan.
We are given:
$$\begin{cases}
A_p=60,000\\
n=12\cdot 30=360\\
i=\dfrac{0.09}{12}=0.0075.
\end{cases}$$
We will use the formula:
$$R=\dfrac{iA_p}{1-(1+i)^{-n}},$$
with $Ap=60,000$, $i=0.0075$ and $n=360$:
$$R=\dfrac{0.0075(60000)}{1-(1+0.0075)^{-360}}\approx 482.77.$$
b) We are given:
$$\begin{cases}
A_p=60,000\\
n=12\cdot 15=180\\
i=\dfrac{0.09}{12}=0.0075.
\end{cases}$$
We will use the formula:
$$R=\dfrac{iA_p}{1-(1+i)^{-n}},$$
with $Ap=60,000$, $i=0.0075$ and $n=180$:
$$R=\dfrac{0.0075(60000)}{1-(1+0.0075)^{-180}}\approx 608.56.$$
