Respuesta :
Answer:
number of payment is 3.05 payment
so correct option is b 3.05 payments
Explanation:
balance = $5000
annual rate r1 = 18.7 % = [tex]\frac{0.187}{12}[/tex] = 0.01558
credit card charging r2 = 5.9% = [tex]\frac{0.059}{12}[/tex] = 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 = [tex]P * \frac{1-(1+r)^{-t}}{r}[/tex] ...........................1
here P is payment and t is time and r is rate
put here all value and find t for r1
balance = [tex]P * \frac{1-(1+r)^{-t}}{r}[/tex]
5000 = [tex]250 * \frac{1-(1+0.01558)^{-t}}{0.01558}[/tex]
take log both side
log 0.6884 = log 1 - log[tex](1+0.01558)^{t}[/tex]
t = 24.1519 .................2
and now put here all value and find t for r2
balance = [tex]P * \frac{1-(1+r)^{-t}}{r}[/tex]
5000 = [tex]250 * \frac{1-(1+0.00492)^{-t}}{0.00492}[/tex]
take log both side
log 0.9016 = log 1 - log[tex](1+0.00492)^{t}[/tex]
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
