Question

Joshua purchases a $2,100 couch on a credit card that charges 18% annual interest, where interest is compounded monthly. Assuming Joshua make the minimum monthly payment of $50 each month, how many months will it take him to pay off this couch?

Answer 1

Monthly interest rate = 18/12 = 1.5% or 0.015

Monthly payment, C = $50

Using the formula for present value of the equivalent cashflows, we get

2100 = 50 * [(1 - 1/(1+0.015)^n)/0.015]
=> 42 *0.015 = 1 - 1/(1 + 0.015)^n

=> (1+0.015)^n = 2.7027

Apying ln (natural log) on both the sides,

n*ln(1.015) = ln(2.7027)

=> n = 66.8 or 67 months

Thus, 67 months are required by him to pay for hia couch.

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