Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent.
P = 23,000, r = 3, t = 12, m = 3

A) R = $763.93
B) R = $799.41
C) R = $706.58
D) R = $740.40

Question

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
P = 23,000, r = 3, t = 12, m = 3
​
A) R = $763.93
B) R = $799.41
C) R = $706.58
D) R = $740.40

Quizplus · Accepted Answer

The formula for the periodic payment R is given by:  $$ R = \frac{P \cdot \frac{r/m}{1 - (1 + r/m)^{-mt}}}{1 - (1 + r/m)^{-mt}} $$  Substituting the given values:  $$ P = 23000, \ r = 0.03, \ t = 12, \ m = 3 $$  $$ R = \frac{23000 \cdot \frac{0.03/3}{1 - (1 + 0.03/3)^{-36}}}{1 - (1 + 0.03/3)^{-36}} $$  Calculating this gives R approximately equal to $763.93.

Find the Periodic Payment R Required to Amortize a Loan