Your VISA bill for September has one item: a 72 inch Plasma television costing $

Question

Your VISA bill for September has one item: a 72 inch Plasma television costing $4,124 which was purchased on Sept. 15th. It is now Oct. 15th at midnight. You have missed the payment deadline and now owe interest. VISA calculates interest on the daily balance (with daily compounding) from the date of purchase. Assume that the purchase occured at midnight, so the Sept. 15th purchase accrues its first day of interest at the end of Sept. 16th. The annual rate charged by VISA is 19.2%. If you pay off the debt (including interest) right now (at midnight on Oct. 15th), then how much do you have to pay? (Assume a 365-day year). Round to the nearest cent. *Show work please! Thank you!*

Explanation / Answer

Since, today is October 15th mid-night and the interest for first day will get accrued at the end of September 16th, the total number of days for which the interest payment will have to be made would be 30 (as we will include the interest for September 16th and the interest will become due till October 15the midnight). The entire amount is being paid on October 15th midnight, so the interest for 15th will not become due. The total amount to be paid today can be calculated with the use of following formula:

Amount = Principal*(1+Interest Rate/365)^n where n would represent number of days for which interest is due

__________

Here, Principal = $4,124, Interest Rate = 19.20% and n = 30

Using these values in the above formula, we get,

Amount = 4124*(1+19.20%/365)^30 = $4,189.58 (so, the interest amount is $65.58)

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