SOLUTION: Your credit card has a balance of $6100 and an annual interest rate of 19%. You decide to pay off the balance over four years. If there are no further purchases charged to th
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Question 1206585: Your credit card has a balance of $6100 and an annual interest rate of 19%. You decide to pay off the balance over four years. If there are no further purchases charged to the card, you must pay $182.42 each month, and you will pay a total interest of $2656.16. Assume you decide to pay off the balance over one year rather than four. How much more must you pay each month and how much less will you pay in total interest? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! i used the texas instruments business analyst 2 calculator to help analyze this.
there are some discrepancies that make analysis a little more difficult than it should be.
the problem:
19% annual interest compounded monthly equals 1.5833333....% monthly effective interest rate.
that results in a monthly payment of 182.3907211.
your monthly payment is 182.42 which i presume has been rounded to the nearest penny.
to get a monthly payment equal to 182.42, i had to play with the interest rate per month.
i got an interest rate per month of 1.584091296%.
i decided to use that so that i could match your results.
using that interest rate per month, i got:
payment at the end of each month = 182.42.
total payments = 48 * 182.42 = 8756.16.
total interest = 8756.16 minus 6100 = 2656.16.
that puts us in agreement on the basic figures quoted.
if you decided to pay off the loan in one year rather than four, using the same interest rate i calculated to match your initial figures, i get:
payment at the end of the month = 562.1816071 which we can round off to 562.18.
total payments = 12 * 562.18 = 6746.16.
total interest = 6746.16 minus 6100 = 646.16.
i used an online calculator that provides similar results, only it rounds the answers to the nearest penny.
it provides an answer that can be right on, but can also be off by a small amount because of intermediate rounding.
here's what that financial calculator shows.
the first shows the calculation of the monthly interest rate that gets you a monthly payment of 182.42.
the second shows the calculation of the monthly interest rate when you drop the length of the loan from 4 years (48 months) to 1 year (12 months).
bottom line:
your problem questions were:
How much more must you pay each month and how much less will you pay in total interest?
your solution is:
you would pay 590.18 minus 182.42 = 407.76 more per month.
you would pay 2656.16 minus 646.16 = 2010.00 less total interest.
