Find the periodic payment required to repay $1,940 repaid in 15 monthly installments, at an annual rate of 13%.Round to the nearest cent.
A) $\quad P = \$ 190.83$
B) $P = \$ 281.64$
C) $\quad P = \$ 140.82$
D) $\quad P = \$ 314.14$
E) $\quad P = \$ 126.74$

Question

Find the periodic payment required to repay $1,940 repaid in 15 monthly installments, at an annual rate of 13%.Round to the nearest cent. 
A) $\quad P = \$ 190.83$
B) $P = \$ 281.64$
C) $\quad P = \$ 140.82$
D) $\quad P = \$ 314.14$
E) $\quad P = \$ 126.74$

Quizplus · Accepted Answer

To find the periodic payment required, we use the formula for the present value of an annuity:

$1940 = P \cdot \dfrac{1 - (1+i)^{-n}}{i}$

where $P$ is the periodic payment, $i$ is the monthly interest rate (which is $0.13/12$), and $n$ is the total number of payments (which is 15).

Simplifying the equation, we get:

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

Plugging in the values, we get:

$P = \dfrac{0.13/12 \cdot 1940}{1-(1+0.13/12)^{-15}} \approx \$140.82$

Rounding to the nearest cent, we get the answer choice C.

Find the Periodic Payment Required to Repay $1,940 Repaid in 15