To find the compound interest, subtract the principal from the future value calculated using the compound interest formula. Apply the formula with the given values of principal, interest rate, and time, then subtract the principal to determine the compound interest over the given period.
To determine the amount A in an account after T years with principal P and an annual interest rate r compounded continuously, you can use the compound interest formula:
Future Value = Principal x (1 + interest rate)time
For compound interest specifically, the formula becomes:
Compound interest = Future Value - Present Value
To apply this to an example, let's say you have a three-year scenario:
Calculate the Future Value using the compound interest formula with the given values of Principal (P), interest rate (r), and time (t).
Subtract the Principal (P) from the Future Value to find the compound interest earned over the three years.
Using the formula Principal(1 + interest rate)time and inserting the numbers from our example, if you had a $1,000 deposit with an annual interest rate of 2% compounded annually for three years, the calculation would be $1,000(1+0.02)3 = $1,061.21.
The compound interest would then be $1,061.21 - $1,000 = $61.21.
The probable question may be:
To find the amount A in an account after T years with principal P and an annual interest rate r compounded n times per year you can use the formula
To find the amount A in an account after t years with principal P and an annual interest rate r compounded continuously, you can use the formula