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.(2 points)
To the nearest dollar, the total cost of repaying the loan is $__
. The fixed monthly payment amount is $__
. The total amount of interest paid is $__
.
To find the total cost of repaying the loan, we need to calculate the monthly payment amount and multiply it by the number of months in the term.
First, we need to calculate the monthly interest rate by dividing the annual interest rate by 12: 21% / 12 months = 1.75% per month.
Next, we need to calculate the monthly payment amount using the compound interest formula:
M = P * (r*(1+r)^n) / ((1+r)^n -1)
Where:
M = monthly payment amount
P = principal loan amount = $3,500
r = monthly interest rate = 1.75% or 0.0175
n = number of months in the term = 24
M = 3500 * (0.0175*(1+0.0175)^24) / ((1+0.0175)^24 - 1)
M ≈ $172.98
The fixed monthly payment amount is approximately $172.98.
To find the total cost, we multiply the monthly payment amount by the number of months:
Total cost = monthly payment amount * number of months
Total cost = $172.98 * 24
Total cost = $4,151.52
The total cost of repaying the loan is approximately $4,152.
The total amount of interest paid can be found by subtracting the original loan amount from the total cost:
Total interest paid = total cost - loan amount
Total interest paid = $4,152 - $3,500
Total interest paid = $652
The total amount of interest paid is approximately $652.