calculate the final loan amount of a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term.
a $583.20
b $586.14
c $580.00
d $86.14
To calculate the final loan amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $500, the annual interest rate (r) is 16% or 0.16 (as a decimal), the loan is compounded monthly, so n = 12, and the term (t) is 1 year.
Plugging in the values:
A = 500(1 + 0.16/12)^(12*1)
A = 500(1 + 0.01333333)^(12)
A = 500(1.01333333)^(12)
A ≈ 500(1.179363)
A ≈ 589.6815
Therefore, the final loan amount is approximately $589.68. None of the given options match exactly, but the closest is option b, $586.14.