Question

Your trip to was great, but it unfortunately ran a bit over budget. However, you just received an offer in the mail to transfer your $10 000 balance from your current credit card, which charges an annual rate of 19.8%, to a new credit card charging a rate of 6.2%. How much faster could you pay the loan off by making your planned monthly payments of $200 with the new card? What if there was a 2% fee charged on any balances transferred?

Answer 1

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:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $200.00

time n

rate 0.005166667 (6.2% rate divide into 12 months)

PV $10,000.0000

$200 \times \frac{1-(1+0.0051667)^{-n} }{0.0051667} = 10000$

We arrenge the formula and solve as muhc as we can:

$(1+0.0051667)^{-n}= 1-\frac{10000\times0.0051667}{200}$

$(1+0.0051667)^{-n}= 0.74166667$

Now, we use logarithmics properties to solve for time:

$-n= \frac{log0.741667}{log(1+0.0051667)$

-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:

$(1+0.0051667)^{-n}= 1-\frac{10200\times0.0051667}{200}$

$(1+0.0051667)^{-n}=0.73650000$

$-n= \frac{log0.7365}{log(1+0.0051667)$

-59.34880001 = 59.35 months