Question

How long (in months) would it take to pay off a student loan totaling $12,000 if a monthly payment of $300 is made each month and the appropriate rate of interest is 4% annual rate compound monthly?

Please show Step by step

Answer 1

Loan Amount = Monthly Payment * present value annuity factor(Interest per month,total payments)

12000 = 300 * (1 - (1 + r)^-n) / r

r = Interest per month = 4%/12 = 0.33%

n = Number of months

12000 = 300 * (1 - (1 + 0.33%)^-n) / 0.33%

12000 = 90000 * (1 - (1 + 0.33%)^-n)

0.1333 = (1 - (1 + 0.33%)^-n)

1.0033^-n = 0.8667

Apply log on both sides

Log(1.0033^-n) = Log 0.8667

-n * Log (1.0033) = log 0.8667

-n = -0.06215 / 0.001445

n = number of months required to payoff loan balance = 43 Months