Determine the amount of interest charged on S. Carter's account during the second month. S. Carter's account
Principal: $1,604
Rate: 10% compound
Length of period: month
Second month's interest: _________
$13.48 $160.40
$16.04
To determine the amount of interest charged on S. Carter's account during the second month, we need to 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 amount (the initial investment/loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal (P) is $1,604, the annual interest rate (r) is 10% (or 0.10 as a decimal), the length of the period (t) is one month, and the compounding frequency (n) is not given. Therefore, we need to assume the compounding frequency.
Let's assume the compounding frequency is monthly. So, n = 12 (since there are 12 months in a year).
Plugging the values into the formula:
A = 1604(1 + 0.10/12)^(12*1)
A = 1604(1 + 0.008333)^12
A = 1604(1.008333)^12
A ≈ 1604(1.103812)
Calculating A:
A ≈ 1768.03
Now, we need to determine the interest charged during the second month. To do this, we subtract the principal amount from the future value (A).
Interest = A - P
Interest = 1768.03 - 1604
Interest ≈ $164.03
Therefore, the amount of interest charged on S. Carter's account during the second month is approximately $164.03.