Using an online calculator, 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 can use the formula:
Total Cost = Principal + Total Interest
Principal = $3,500
Total Interest can be calculated using the formula for compound interest:
Total Interest = P * (1 + r/n)^(nt) - P
Where:
P = Principal = $3,500
r = interest rate per period = 21% = 0.21
n = number of compounding periods per year = 12 (since it is compounded monthly)
t = number of years = 24/12 = 2
Plugging in the values, Total Interest = 3,500 * (1 + 0.21/12)^(12*2) - 3,500
Total Interest = 3,500 * (1 + 0.0175)^(24) - 3,500
Total Interest = 3,500 * (1.0175)^(24) - 3,500
Total Interest ≈ 3,500 * 1.4761 - 3,500
Total Interest ≈ 3,500 * 0.4761
Total Interest ≈ 1665.35
Total Cost = 3,500 + 1665.35
Total Cost ≈ 5,165.35
To find the fixed monthly payment amount, we can use the formula:
Fixed Monthly Payment = Total Cost / number of months
Number of months = t * n = 2 * 12 = 24
Fixed Monthly Payment = 5,165.35 / 24
Fixed Monthly Payment ≈ 215.22
To find the total amount of interest paid, we can subtract the principal from the total cost:
Total Interest Paid = Total Cost - Principal
Total Interest Paid ≈ 5,165.35 - 3,500
Total Interest Paid ≈ 1,665.35
Therefore, the nearest dollar values are:
The total cost of repaying the loan is $5,165.
The fixed monthly payment amount is $215.
The total amount of interest paid is $1,665.