Calculate the final loan amount of a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term.
(1 point)
$580.00
$583.20
$86.14
$586.14
To calculate the final loan amount, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final loan amount
P = principal amount (initial loan amount)
r = annual interest rate (in decimal form)
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 interest is compounded monthly (n = 12), and the loan term is 1 year (t = 1).
Using this information, we can calculate the final loan amount (A):
A = 500(1 + 0.16/12)^(12*1)
A = 500(1 + 0.013333)^12
A = 500(1.013333)^12
A ≈ 500(1.183136) = $591.57
Rounded to the nearest cent, the final loan amount is approximately $591.57.
None of the answer choices provided match this calculated amount, so it seems there may be an error in either the provided answer choices or the information given.