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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 loan 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:
P = $500
r = 16% = 0.16 (decimal form)
n = 12 (compounded monthly)
t = 1 year
Now plug in the values into the formula:
A = 500(1 + 0.16/12)^(12*1)
A = 500(1 + 0.0133)^12
A = 500(1.0133)^12
A = 500(1.179498)[approx.]
A ≈ $589.74
So, the final loan amount of a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term, is approximately $589.74.