Problema Solution
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.)
Answer provided by our tutors
base price = $435
r = 0.094 or 9.4% annual rate
n = 12 compounding periods per year (compounded monthly)
t = 1.5 year
total price = sales tax value + base price = 0.0851*435 + 435 = 37.01 + 435 = $472.02
P = $472.02 is the principle
we need to find the future value FV:
FV = P(1 + r/n)^(n*t)
FV = 472.02(1 + 0.094/12)^(1.5*12)
FV = 472.02*(1+ 0.094/12)^18
FV = $543.20
Brian paid $543.20 in total.