SOLUTION: Derek used his credit card to buy a hay ride for him and his friends. The ride cost $500 plus 5% GST. He did not pay his bill within the grace period and must pay interest on his b

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Question 1104576: Derek used his credit card to buy a hay ride for him and his friends. The ride cost $500 plus 5% GST. He did not pay his bill within the grace period and must pay interest on his bill. The interest rate is 15% compounded daily from the date of purchase.
A) What is the total amount of hay ride with taxes?
B) At $120 per month, how long will it take Derek to pay off the balance?
C) How much will he pay in interest, paying $120 monthly?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the cost of the hay ride is 500.
general sales tax is 5%.
the total cost is 500 + .05 * 500 = 525.

he pays 120 at the end of each month until the debt is eliminated.

i calculate that it will take him 4.528196438 months to pay it off.

the interest rate is compounded daily and the payments are made monthly.

i used the TI Business Analyst II.

i assumed 365 days in a year.

using that calculator, i set P/Y = 12 and C/Y = 365

P/Y is payments per year.
C/Y is compounding periods per year.

i then made the following entries.

PV = 525
PMT = -120
FV = 0
I/Y = 15%

i then had the calculator tell me the number of months.

the calculator came back and said that the number of months required to pay off the loan was 4.528196438.

i then verified with the nper function of excel by entering the following:

rate = (1 + .15/365)^(365/12) - 1
pv = 525
pmt = -120
fv = 0
payments made at the end of the time period.

i got the same answer.

i'm not sure whether this answer will satisfy your requirements because the answer depends heavily on the assumptions used, but this is a reasonable answer as best as i can determine.

the number of months required is slightly more than if you used monthly compounding.

with monthly compounding, the number of months required came out to be 4.527239105.

with daily compounding, the number of months required came out to be 4.528196438.

the equivalent monthly interest rate for monthly compounding was .15/12 = .0125

the equivalent monthly interest rate for daily compounding was (1+ .15/365)^(365/12) - 1 = .012575851.

the use of a calculator that allows you to do compounding periods different from payment periods is recommended.