Question

Suppose that you have a $2,000 balance on a credit card with a 7.99% annual interest rate, and you can afford to pay $150 per month toward this debt.

a. Find the amount of time it takes to pay off this debt. Give your answer in months and years.
b. Calculate the total amount paid over the life of the debt.

Answer 1

loan is paid in 1 year 3 months

total amount paid over life = $2101.35

Explanation:

given data

balance = $2,000

annual interest rate = 7.99%

afford to pay = $150 per month

solution

we apply formula for amount of time to pay off debit is

`amount(1+ (rate)^t) - principal( (1-(1+rate)^t)/(-rate) )` = 0 ...........1

here rate is
`(0.0799)/(12)` per month

and t is time that is find here

put here all value

`2000(1+ ((0.0799)/(12))^t) - 150( (1-(1+(0.0799)/(12))^t)/(-(0.0799)/(12)) )` = 0

`(1+ (0.0799)/(12))^t ((799)/(9000)  - 1 ) = -1`

take log both side

t × log (
`1+ (0.0799)/(12)` ) = - log (
`(8201)/(9000)` )

t = 14.009

so loan is paid in 1 year 3 months

and

total amount paid over life of debit is

total amount paid over life = $14.009 × 150

total amount paid over life = $2101.35