The total amount of interest on a $6000 loan with a 19% annual interest rate compounded annually is $1140.
To calculate the total amount of interest on the loan, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the total future amount, including principal and interest
- P is the initial principal amount (the borrowed amount)
- r is the annual interest rate (as a decimal)
- n is the number of times that interest is compounded per year
- t is the number of years
In this case, the initial principal amount (P) is $6000, the annual interest rate (r) is 19% (or 0.19 as a decimal), and the loan is compounded annually (n = 1).
Since the loan is not being paid off, the total future amount (A) after a certain number of years will be the borrowed amount plus the accumulated interest. To find the total amount of interest, we subtract the initial principal amount from the total future amount:
Total Interest = A - P
Let's calculate the total interest:
P = $6000, r = 0.19, n = 1, t = 1
A = $6000(1 + 0.19/1)^(1*1) = $6000(1 + 0.19)^1 = $6000(1.19) = $7140
Total Interest = $7140 - $6000 = $1140