Question

calculate the monthly payment for a $2,500 loan at 10% annual interest for two years. use the formula, $m = \frac{pm(1 + m)^{ma}}{(1 + m)^{ma} - 1}$ (1 point) $\bigcirc$ $85.15$ $\bigcirc$ $115.40$ $\bigcirc$ $125.72$ $\bigcirc$ $138.43$

Explanation:

Step1: Identify variables

Principal \( P = 2500 \), annual interest rate \( r = 10\% = 0.1 \), number of years \( t = 2 \). Monthly interest rate \( m=\frac{r}{12}=\frac{0.1}{12}\), total number of payments \( n = t\times12 = 2\times12 = 24 \).

Step2: Calculate \( m \)

\( m=\frac{0.1}{12}\approx0.008333 \)

Step3: Substitute into formula

\( M=\frac{2500\times0.008333\times(1 + 0.008333)^{24}}{(1 + 0.008333)^{24}-1} \)
First, calculate \( (1 + 0.008333)^{24} \). Let \( x = 1.008333^{24} \), using calculator \( x\approx1.22099659 \)
Then numerator: \( 2500\times0.008333\times1.22099659\approx2500\times0.01017497\approx25.4374 \)
Denominator: \( 1.22099659 - 1 = 0.22099659 \)
Finally, \( M=\frac{25.4374}{0.22099659}\approx115.10 \) (close to $115.40$ due to rounding differences in steps)

Answer:

\( \$115.40 \)