Question

You just received an offer in the mail to transfer your $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 5.9 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. 2.36 paymentsb. 3.05 paymentsc. 3.10 paymentsd. 2.79 paymentse. 2.86 payments

Answer 1

Answer:

number of payment is 3.05 payment

so correct option is b 3.05 payments

Explanation:

balance = $5000

annual rate r1 = 18.7 % = $\frac{0.187}{12}$ = 0.01558

credit card charging r2 = 5.9% = $\frac{0.059}{12}$ = 0.004917

payments P = $250  month

to find out

How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card

solution

we first find time t both rate by total balance formula that is

balance =  $P * \frac{1-(1+r)^{-t}}{r}$    ...........................1

here P is payment and t is time and r is rate

put here all value and find t for r1

balance =  $P * \frac{1-(1+r)^{-t}}{r}$  

5000 =  $250 * \frac{1-(1+0.01558)^{-t}}{0.01558}$

take log both side

log 0.6884 = log 1 - log$(1+0.01558)^{t}$    

t = 24.1519        .................2

and now put here all value and find t for r2

balance =  $P * \frac{1-(1+r)^{-t}}{r}$  

5000 =  $250 * \frac{1-(1+0.00492)^{-t}}{0.00492}$

take log both side

log 0.9016 = log 1 - log$(1+0.00492)^{t}$  

t = 21.1055         .....................3

so by equation 2 and 3

so no of payment will be 24.1519 - 21.1055

so number of payment is 3.05 payment

so correct option is b 3.05 payments