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)
Responses
$86.14
$86.14
$583.20
$583.20
$586.14
$586.14
$580.00
To calculate the final loan amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final loan amount
P = principal amount (initial loan amount)
r = interest rate per period (in decimal form)
n = number of compounding periods per year
t = number of years
In this case:
P = $500
r = 16% = 0.16
n = 12 (compounded monthly)
t = 1 year
Plugging in these values into the formula, we get:
A = 500(1 + 0.16/12)^(12*1)
A = 500(1 + 0.013333)^12
A = 500(1.013333)^12
A = 500(1.179869)
Calculating the final loan amount, we get:
A ≈ $589.93
Therefore, the closest answer is $586.14.