Question

You have a credit card with a balance of $10,900 and an APR of 17.1 percent compounded monthly. You have been making monthly payments of $215 per month, but you have received a substantial raise and will increase your monthly payments to $265 per month. How many months quicker will you be able to pay off the account

Answer 1

Approximately 15 months quicker

Step-by-step explanation:

A = PMT(1+r/100)^t

where r = monthly rate = 17.1/12=1.425%

t= time in months

PMT = monthly payments

A= Amount = $10,900

Case 1; At PMT of $215

Therefore,

10,900 = 215(1 + 0.01425)^t

1.01425^t= 50.7

Solving for t, t= 277.46 months

Case 2; At PMT of $265

Therefore,

10,900 = 265(1 + 0.01425)^t

1.01425^t= 41.13

Solving for t, t= 262.68 months

The months quicker = 277.46 - 262.68 = 14.78 months

Approximately 15 months quicker

Answer 2

months quicker = 91 months - 62 months = 29 months

Step-by-step explanation:

using a financial calculator

SET calculator to a 12 months interval payments

PV = -$10.900, r= 17.1%, FV=0, ,PMT = $215

COMPUTE N?

N= 90.58 ≈ 91 months

Raise and new pmt =265

N=62.35≈62 Months