Question

Your credit card has a balance of $550 and an annual interest rate of 17%. With no further purchases charged to the card and the balance being paid off over five years, the monthly payment is ?$137?, and the total interest paid is ?$2720. You can get a bank loan at 9.5% with a term of six years.

a. How much will you pay each? month? How does this compare with the? credit-card payment each? month?

Select the correct choice below and fill in the answer boxes within your choice.

option A. The monthly payments for the bank loan are approximately $___. This is $___ more than the monthly credit-card payments.

option B. The monthly payments for the bank loan are approximately $___. This is $___ less than the monthly credit-card payments.

b. How much total interest will you? pay? How does this compare with the total? credit-card interest?

Select the correct choice below and fill in the answer boxes within your choice.

option A. The total interest paid over 6 years for the bank loan is approximately $___. This is $___ more than the total credit-card interest.

option B. The total interest paid over 6 years for the bank loan is approximately $___. This is $___ less than the total credit-card interest.

Answer 1

Answer a:

option B. The monthly payments for the bank loan are approximately $101. This is $36 less than the monthly credit-card payments.

Working:

Given:

Monthly Credit card payment = $137

Monthly bank loan payment is calculated below:

EMI = [P x R x (1+R)^N]/[(1+R)^N-1],

where P = Principal,

R = interest rate per month

N = Number of monthly installments

EMI = [$5,500 * 9.5%/12 * (1+9.5%/12)⁷²] / [(1+9.5%/12)⁷² - 1]

=$101 (rounded off to nearest dollar)

Hence monthly payment of bank loan = $101 and the same is ($137 - $101=) $36 less than the monthly credit card payment.

Answer b:

option B. The total interest paid over 6 years for the bank loan is approximately $1,737. This is $983 less than the total credit-card interest.

Workings:

Given:

The total credit card interest paid is $2,720

The total interest paid over 6 years for the bank loan is $1,737 (as calculated below from repayment schedule over 6 years).

Hence total interest paid over 6 years for the bank loan is ($2,720 - $1,737=) $983 less than the total credit-card interest.