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,
[tex]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 \frac{11.80646 - 11.64497}{0.00353}\\\\n \approx \frac{0.16149}{0.00353}\\\\n \approx 45.74788\\\\n \approx 46[/tex]
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
