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Trisha uses her credit card to pay for new tires that ended up totaling $527.89. She can pay off up to $200 a month. The card has an annual rate of 22.5%. How much will she pay in interest?
 Jan 28, 2014
 #1
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AMaqueira3:

Trisha uses her credit card to pay for new tires that ended up totaling $527.89. She can pay off up to $200 a month. The card has an annual rate of 22.5%. How much will she pay in interest?



I will take a small detour before explaining the question to you,

Remember that if she'd borrow this amount for 3 years without paying off anything in the mean time, she would have to pay $527.89*(1.225) 3 at the end of the three years. The interest she'd have to pay in three years would then thus equal (1.225) 3-1 which is aproximately 0.838 or similarily 83.8%

Now we can do the same thing to calculate the interest Trisha has to pay every month. Since a year has 12 months, the interest per month will equal 1.225 (1/12)-1 = 0.017 or 1.7%.

To continue, look at it on a month to month basis


Then in month 0 she pays the $527.89

in month 1 she has interest of $527.89*0.017 = 9.00 which amounts her total debt to 536.89,
However she pays of 200 which makes her debt 336.89

Now for month 2 she has interest of $336.89*0.017 = 5.73 which amounts her total debt to ....

I think you can finish this part yourself from there on, stop when she has paid off all her debt.

Now to answer the question, you have to add up all the interest she has had to pay, so 9.00 + 5.73 + etc

Good luck
 Jan 28, 2014
 #2
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AMaqueira3:

Trisha uses her credit card to pay for new tires that ended up totaling $527.89. She can pay off up to $200 a month. The card has an annual rate of 22.5%. How much will she pay in interest?



Hi AMaqueira3 and Reiner-g

Reiner-g, i think that you have made this question more difficult than intended.

Reiner-g has taken 22.5% p.a. to be an effective interest rate whereas I believe it is a nominal annual interest rate.
What Reiner has done is perfectly accurate, it just depends on your interpretation of the question.

I think that the interest rate is a nominal 22.5%pa due monthly. Which means that the effective interest rate is 22.5/12 = 1.875% per month.
1.875% = 0.01875
After that we are in agreement
After 1 month interest
Interest = 0.01875*527.89 = 9.89
Amount owing = original amount + interest = $527.89+9.89 = $537.78
-------------------------------------------------
Instead of doing it in 2 steps like that I could just say that the new amount would be 100% of the original value + another 1.875% of the interest
That is, after 1 month (but before making a payment) you Trisha will owe 101.875% of $527.89 = 1.01875 x $527.89 = $537.78
-------------------------------------------------------------
so at the end of the 1st month Trisha will owe $537.78 - the $200 payment = $337.78
at the end of th 2nd month Trisha will owe 1.01875*337.78 - 200 = $144.11
work out how much she owes at the end of the 3rd month. Her payment will be less than $200 - she won't owe that much.
Add up how much she paid back take away the original cost and that would have to be the interest.
If not for the difference in the interest rate, Reiner's answer would be the same.
 Jan 29, 2014
 #3
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0
Fair point Melody,

I do agree 22.5%/12 is indeed more accurate for this question
 Jan 29, 2014

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