Final answer:
To find the amount accumulated from a $500 certificate of deposit with 4¼% interest compounded continuously over 3 years, the continuous compounding formula A = P * e^(rt) is applied, resulting in approximately $568.09.
Step-by-step explanation:
If a $500 certificate of deposit earns 4¼% interest compounded continuously, the amount accumulated at the end of a 3-year period is calculated using the formula for continuous compounding: A = P * e^(rt).
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- t = the time the money is invested for, in years.
- e = Euler's number (approximately 2.71828).
First, we will convert the interest rate from a percentage to a decimal by dividing by 100: 4¼% = 4.25% = 0.0425.
Next, we use the formula to find the accumulated amount:
A = 500 * e^(0.0425*3)
Now we can calculate the exact amount.
A = 500 * e^(0.1275)
A = 500 * (approximately 1.13618)
A = approximately $568.09
Therefore, the certificate of deposit will accumulate to approximately $568.09 at the end of a 3-year period.