Question

You just received an offer in the mail to transfer the $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 7.9 percent. You plan to make payments of $250 a month on this debt. How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card?

A) 2.48 payments

B) 2.63 payments

C) 3.10 payments

D) 2.79 payments

E) 2.86 payments

Please provide answer and how to solve it by hand and by BA II Plus calculator method.

Answer 1

Monthly Rate = annual rate /12= 18.7%/12= 1.558%

Monthly payment =c= 250

Loan balance = 5000

Total balance = C × (1- 1/(1+R)^t /R)

5000= 250× (1-1/(1+0.01558)^t/0.01558)

5000/250= 1-1/(1+0.01558)^t/0.01558)

20×0.01558 = 1-1/(1+0.01558)^t

1/(1+0.01558)^t= 0.6884

Both side log

-t= log 0.6884/ (1+0.01558)

t= 24.1519

Find the t when the annual interest rate 7.9%

Monthly rate = 7.9%/12= 0.658%

5000= 250× (1-1/(1+0.00658)^t/0.00658)

5000/250= 1-1/(1+0.00658)^t/0.00658)

20×0.00658 = 1-1/(1+0.00658)^t

1/(1+0.00658)^t= 0.8684

Both side log

-t= log 0.8684 / log (1.00658)

t= 21.5147

Number of payment =24.1519-21.5147= 2.63