Brian bought a new air conditioning unit on his credit card. The unit had a base price of $435. Brian made no other purchases on his credit card. Brian's credit card has an interest rate of 9.4%, compounded monthly, and Brian paid off the balance by making monthly payments for a year and a half. If the sales tax in Brian's area is 8.51%, how much did Brian pay in total? (Round all dollar values to the nearest cent.) a. $472.02 b. $468.00 c. $496.32 d. $507.96

Question

Mathematics

Cubby

6 April, 00:15

Brian bought a new air conditioning unit on his credit card. The unit had a base price of $435. Brian made no other purchases on his credit card. Brian's credit card has an interest rate of 9.4%, compounded monthly, and Brian paid off the balance by making monthly payments for a year and a half. If the sales tax in Brian's area is 8.51%, how much did Brian pay in total? (Round all dollar values to the nearest cent.) a. $472.02 b. $468.00 c. $496.32 d. $507.96

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Morgan · Answer 1

Given:

Unit base price: $435

Credit Card interest rate, i = 9.4% compounded monthly; i = 0.00783/month comp monthly

n = 1.5 years = 18 months

sales tax = 8.51%

First, determine the actual price of the unit by adding the sales tax to the base price of the unit:

$435 * (1 + 0.0851)

Actual price = $472.0185

So, the total amount paid by Brian should be higher than the actual price since he used his credit card. Use the formula from economics:

F = P (1+i) ^n

F = $507.96

Therefore, the total amount paid by Brian is $507.96.