A bank credit card charges interest at the rate of
2
3
%
per year, compounded monthly. If a senior in college charges $
1
,
7
0
0
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 will have to pay, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = total amount
P = principal amount (initial amount borrowed) = $1,700
r = annual interest rate = 2/3% = 0.02/12
n = number of times interest is compounded per year = 12
t = time the money is borrowed for (in years) = 1
Plugging in the values, we get:
A = $1,700(1 + 0.02/12)^(12*1)
A = $1,700(1 + 0.00166667)^12
A = $1,700(1.00166667)^12
A ≈ $1,700 * 1.0200361
A ≈ $1,734.06
Therefore, the senior will have to pay approximately $1,734.06 in total after one year.