Given:

P (Principal) = $9,500

Annual interest rate = 7.25%

r (Monthly interest rate) = 7.25%12\frac{7.25%}{12}127.25%​ = 0.072512≈0.00604167\frac{0.0725}{12} \approx 0.00604167120.0725​≈0.00604167

n (Total number of payments) = 5 years ×\times× 12 months/year = 60 months

The formula for the monthly payment MMM is:

M=P×r×(1+r)n(1+r)n−1M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}M=(1+r)n−1P×r×(1+r)n​

Substituting the given values:

M=9500×0.00604167×(1+0.00604167)60(1+0.00604167)60−1M = \frac{9500 \times 0.00604167 \times (1 + 0.00604167)^{60}}{(1 + 0.00604167)^{60} - 1}M=(1+0.00604167)60−19500×0.00604167×(1+0.00604167)60​

Step-by-Step Calculation:

Step 1: Calculate (1+r)60(1 + r)^{60}(1+r)60:

(1+0.00604167)60≈1.42576(1 + 0.00604167)^{60} \approx 1.42576(1+0.00604167)60≈1.42576

Step 2: Calculate the numerator:

9500×0.00604167×1.42576≈81.9469500 \times 0.00604167 \times 1.42576 \approx 81.9469500×0.00604167×1.42576≈81.946

Step 3: Calculate the denominator:

1.42576−1=0.425761.42576 - 1 = 0.425761.42576−1=0.42576

Step 4: Calculate the monthly payment MMM:

M=81.9460.42576≈192.43M = \frac{81.946}{0.42576} \approx 192.43M=0.4257681.946​≈192.43