Answer:
[tex]\large \boxed{\$1127.28}[/tex]
Explanation:
For an amortized loan, paying back a fixed amount periodically, the formula for each payment is
a = P\left (\dfrac{r(1 + r)^{n}}{(1 +r)^{n} - 1}
where
a = payment amount per period
P = principal (loan amount)
r = interest rate per period
n = total number of periods (payments)
Data:
Cost = $68 000
Down payment = $20 000
Term of loan = 4 yr
APR = 6 %
Payments = monthly
Calculations:
P = $68 000 - $20 000 = $48 000
n = 4 × 12 = 48
r = 0.06/12 = 0.005
[tex]\begin{array}{rcl}a&=& 48000\left (\dfrac{0.005(1 +0.005)^{48}}{(1 + 0.005)^{48} - 1} \right )\\\\&=& 48000\left (\dfrac{0.005(1.005)^{48}}{(1.005)^{48} - 1} \right )\\\\&=& 48000\left (\dfrac{0.005 \times 1.270489}{1.2704892 - 1} \right )\\\\&=& 48000\left (\dfrac{0.006352446}{0.2704892} \right )\\\\& =& 480000\times 0.02348503\\\& =& \mathbf{\$1127.28}\\\\\end{array}\\\text{Their monthly payments will be $\large \boxed{\mathbf{\$1127.28}}$}[/tex]
