determine the total cost, fixed monthly payment, and the total interest paid when repaying a credit card loan of $3,500 with a 21% interest rate compounded monthly over a 24 month term. round the answer to the nearest dollar.
To determine the total cost, we first need to calculate the monthly interest rate.
The monthly interest rate can be found by dividing the annual interest rate by 12 (the number of months in a year): 21% / 12 = 1.75%.
Next, we calculate the total cost by adding the principal loan amount to the total interest paid. The principal loan amount is $3,500.
To calculate the total interest paid, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount (principal + interest)
P = Principal loan amount ($3,500)
r = Annual interest rate (21%)
n = Number of times the interest is compounded per year (12)
t = Number of years (24 months / 12 months per year = 2 years)
Using the formula, we have:
A = 3500(1 + 0.0175/12)^(12*2)
Calculating this gives us:
A = 3500(1.001458333)^24
A ≈ 3975.54
The total cost is $3,975.
To find the fixed monthly payment, we divide the total cost by the number of months:
Fixed monthly payment = Total cost / Number of months
Fixed monthly payment = $3,975 / 24
Fixed monthly payment ≈ $165.63
To find the total interest paid, we subtract the principal loan amount from the total cost:
Total interest paid = Total cost - Principal loan amount
Total interest paid = $3,975 - $3,500
Total interest paid = $475
Rounded to the nearest dollar, the total cost is $3,976, the fixed monthly payment is $166, and the total interest paid is $475.