Monthly Payment for the Loan

To calculate the monthly payment for the loan, we use the formula for the monthly payment of an amortized loan:

M=P⋅r⋅(1+r)n(1+r)n−1M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n – 1}M=(1+r)n−1P⋅r⋅(1+r)n​Where:

• $M$ is the monthly payment,
• $P$ is the loan amount ($P=13,500$),
• $r$ is the monthly interest rate (annual interest rate divided by 12),
• $n$ is the total number of payments (number of years multiplied by 12).

Step 1: Assign values

• $P=13,500$
• Annual interest rate = 4.125% = 0.04125
• Monthly interest rate r=0.0412512≈0.0034375r = \frac{0.04125}{12} \approx 0.0034375r=120.04125​≈0.0034375
• Number of years = 3, so $n=3\times 12=36$.

Step 2: Substitute into the formula

M=13,500⋅0.0034375⋅(1+0.0034375)36(1+0.0034375)36−1M = \frac{13,500 \cdot 0.0034375 \cdot (1 + 0.0034375)^{36}}{(1 + 0.0034375)^{36} – 1}M=(1+0.0034375)36−113,500⋅0.0034375⋅(1+0.0034375)36​Let me compute this.

The monthly payment for the loan is $399.32. ​

A logo design company purchases four new computers for $13,500. The company finances the cost of the computers for 3 years at an annual interest rate of 4.125% compounded monthly. Find the monthly payment (in dollars) for this loan. (Round your answer to the nearest cent. See Example 8 in this section.)