Question

How many months will it take you to pay off a loan of $20,000 at 5% APR compounded monthly if you make monthly payments of $825?

Answer 1

This question requires application of PV of annuity formula, according to which

PV =

[1-(4+5)-) [1-(1+r)-n LT P= Periodic Payment r=rate per period n = number of periods

r = 5%/12 = 0.4167% (per month), P = $825, PV = $20,000

1-(1+0.004167)- 20000 = 825 * - | 0.004167

0.10101 = 1 - (1.004167)^-n

(1.004167)^-n = 0.89899

Taking log of both sides

-n * LN(1.004167) = ln(0.89899)

-n * 0.004158 = - 0.10648

n = 25.61 months