A bank credit card charges interest at the rate of 23% per year, compounded monthly. If a senior in college charges $1700
to pay for college expenses, and intends to pay it in one year, what will he have to pay?
Round your answer to the nearest cent.
To calculate the total amount the senior in college will have to pay after one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial charge on the credit card)
r = annual interest rate (23% or 0.23)
n = number of times the interest is compounded per year (monthly compounding means n = 12)
t = time the money is invested/borrowed for (1 year)
Plugging in the values:
A = $1700(1 + 0.23/12)^(12*1)
A = $1700(1 + 0.019167)^12
A = $1700(1.019167)^12
A = $1700(1.238218)
A = $2107.771
Therefore, the senior in college will have to pay approximately $2,107.77 after one year of charging $1700 on the credit card.