Purchase price of article = $5,555
Down payment = $555
Number of payments = 42
True annual interest rate=18%
Monthly Payment= $
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140.99 using $5000.
156.64 using $5555.
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To calculate the monthly payment, we'll use the formula for calculating the monthly payment on a loan:
Monthly Payment = (Purchase Price – Down Payment) * (Monthly Interest Rate / (1 – (1 + Monthly Interest Rate)^(-Number of Payments)))
First, let's calculate the monthly interest rate:
Monthly Interest Rate = True Annual Interest Rate / 12 = 18% / 12 = 0.18 / 12 = 0.015
Now, let's substitute the values into the formula:
Monthly Payment = ($5,555 - $555) * (0.015 / (1 - (1 + 0.015)^(-42)))
Next, we'll calculate the complex part of the formula:
(1 + 0.015)^(-42) ≈ 0.460
Now, we can substitute this value back into the formula:
Monthly Payment = ($5,555 - $555) * (0.015 / (1 - 0.460))
Calculating the values separately:
Purchase Price – Down Payment = $5,000
1 - 0.460 = 0.540
Substituting these values back into the formula:
Monthly Payment ≈ $5,000 * (0.015 / 0.540)
Calculating the division:
Monthly Payment ≈ $138.89
Therefore, the monthly payment for this loan is approximately $138.89.