Find the periodic payment required to repay $27,480 over 12 years, with monthly payments at a 9% annual rate.Round to the nearest cent.
A) $\quad P = \$ 400.25$
B) $\quad P = \$ 444.01$
C) $\quad P = \$ 312.73$
D) $\quad P = \$ 268.97$
E) none of the above

Question

Find the periodic payment required to repay $27,480 over 12 years, with monthly payments at a 9% annual rate.Round to the nearest cent. 
A) $\quad P = \$ 400.25$
B) $\quad P = \$ 444.01$
C) $\quad P = \$ 312.73$
D) $\quad P = \$ 268.97$
E) none of the above

Quizplus · Accepted Answer

First, we need to find the monthly interest rate by dividing the annual rate by 12:

$0.09/12 = 0.0075$

Next, we need to find the total number of payments over 12 years:

$12 	ext{ years} 	imes 12 	ext{ months/year} = 144 	ext{ months}$

Now, we can use the formula for the monthly payment on a loan:

$P = \dfrac{r(PV)}{1-(1+r)^{-n}}$

where:
$P = 	ext{monthly payment}$
$r = 	ext{monthly interest rate}$
$PV = 	ext{present value or amount borrowed}$
$n = 	ext{number of payments}$

Plugging in the values we have:

$P = \dfrac{0.0075(27480)}{1-(1+0.0075)^{-144}} \approx \boxed{\$312.73}$

Therefore, the best choice is C, with a monthly payment of $312.73.

Find the Periodic Payment Required to Repay $27,480 Over 12 P=$400.25\quad P = \$ 400.25P=$400.25

Find the Periodic Payment Required to Repay $27,480 Over 12 $\quad P = \$ 400.25$