Answer:
with the new rate we will pay in 58 months.
if there is 2% commision charge: 59.35 = 60 months
Explanation:
Currently we owe 10,000
This will be transfer to a new credit card with a rate of 6.2%
We are going to do monthly payment of 200 dollars each month
and we need to know the time it will take to pay the loan:
We use the formula for ordinary annuity and solve for time:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $200.00
time n
rate 0.005166667 (6.2% rate divide into 12 months)
PV $10,000.0000
[tex]200 \times \frac{1-(1+0.0051667)^{-n} }{0.0051667} = 10000\\[/tex]
We arrenge the formula and solve as muhc as we can:
[tex](1+0.0051667)^{-n}= 1-\frac{10000\times0.0051667}{200}[/tex]
[tex](1+0.0051667)^{-n}= 0.74166667[/tex]
Now, we use logarithmics properties to solve for time:
[tex]-n= \frac{log0.741667}{log(1+0.0051667)[/tex]
-57.99227477 = 58 months
part B
If there is a charge of 2% then Principal = 10,000 x 102% = 10,200
we use that in the formula and solve:
[tex](1+0.0051667)^{-n}= 1-\frac{10200\times0.0051667}{200}[/tex]
[tex](1+0.0051667)^{-n}=0.73650000[/tex]
[tex]-n= \frac{log0.7365}{log(1+0.0051667)[/tex]
-59.34880001 = 59.35 months
