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

with the new rate we will pay in 58 months.

if there is 2% commision charge: 59.35 = 60 months

Step-by-step 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 * (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 * (1-(1+0.0051667)^(-n) )/(0.0051667) = 10000\\`

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

`(1+0.0051667)^(-n)= 1-(10000*0.0051667)/(200)`

`(1+0.0051667)^(-n)= 0.74166667`

Now, we use logarithmics properties to solve for time:

-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-(10200*0.0051667)/(200)`

`(1+0.0051667)^(-n)=0.73650000`

-59.34880001 = 59.35 months