Question

Suppose you have borrowed $12,000 from a bank with the interest rate of 11.5%. Your monthly installments are $313.07. How long will it take you to pay the loan?

Answer 1

i = 11.5% / 12 = 0.95833% per month

Let n months be period for paying up the loan, then

313.07 * (P/A, 0.95833%,n) = 12000

(P/A, 0.95833%,n) = 12000 / 313.07 = 38.3300859

((1 + 0.0095833)^n-1)/(0.0095833 * (1 + 0.0095833)^n) = 38.3300859

(1.0095833^n-1)/(0.0095833 * 1.0095833^n) = 38.3300859

(1.0095833^n - 1) = 38.3300859 * (0.0095833 * 1.0095833^n)

1.0095833^n - 1 = 0.3673287 * 1.0095833^n

1.0095833^n = 1 / (1 - 0.3673287) = 1.5805996

taking log both sides

n = log 1.5805996 / log 1.0095833 = 47.999 months ~ 48 months