London Motors offers to sell a \$24,000 car for \$470 per month over 60 months. Using the time value of money equation for an ordinary annuity, what is the approximate monthly interest rate (rounded to the nearest tenth of a percent)?

• A. 0.8%
• B. 1.0%
• C. 1.2%
• D. 1.5%

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem. The question involves calculating the monthly interest rate for an ordinary annuity using the time value of money equation. The car's price (\$24,000) is the present value (PV), the monthly payment (\$470) is the annuity payment (PMT), and the number of months (60) is the total number of periods (n). The goal is to find the monthly interest rate (r).
2. Step 2: Recall the formula for the present value of an ordinary annuity: \( PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} \). Here, PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of periods.
3. Step 3: Rearrange the formula to isolate the monthly interest rate (r). This involves iterative or trial-and-error methods since the equation is nonlinear and cannot be solved algebraically for r. Alternatively, financial calculators or software can be used to approximate r.
4. Step 4: Substitute the known values into the formula: \( 24000 = 470 \times \frac{1 - (1 + r)^{-60}}{r} \). Use trial-and-error or a financial calculator to find the value of r that satisfies the equation.
5. Step 5: Once the monthly interest rate (r) is determined, round it to the nearest tenth of a percent as specified in the problem. The correct answer is approximately 1.2%.