Question

6. Bill can afford a monthly payment of $475. He wants to take out a $20,000 loan at 4.25%

interest rate. What should the length of the loan be? Round your answer to the nearest year.

Answer 1

Answer: 4 years

====================================================

Work Shown:

• L = 20,000 = loan amount
• P = 475 = monthly payment
• i = 0.0425/12 = 0.0035417 approximately is the decimal form of the monthly interest rate
• n = unknown number of months

Let A = P/i = 475/0.0035417 = 134116.384787 approximately

Then,

`n = \frac{\text{Ln}(A) - \text{Ln}(A-L)}{\text{Ln}(1+i)}\\\\n \approx \frac{\text{Ln}(134116.384787) - \text{Ln}(134116.384787-20000)}{\text{Ln}(1+0.00354)}\\\\n \approx (11.80646 - 11.64497)/(0.00353)\\\\n \approx (0.16149)/(0.00353)\\\\n \approx 45.74788\\\\n \approx 46`

It will take about 46 months to pay off the loan.

Divide by 12 to convert from months to years.

46 months = 46/12 = 3.83333 years approximately

That rounds to 4 years