Final answer:
Using the formula for continuous compounding interest, the final amount after 5 years is approximately $5525.85 when $5000 is deposited at a 2% interest rate.
Step-by-step explanation:
To calculate the amount of money in an account after a certain period with continuous compounding interest, we use the formula A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), t is the time the money is invested for in years, and e is the base of the natural logarithm, approximately equal to 2.71828.
For a deposit of $5000 at an interest rate of 2% compounded continuously, we need to convert the percentage to a decimal by dividing by 100, which gives us 0.02. Plugging the values into the formula, we get:
A = 5000 * e0.02*5
Calculating this, the final amount should be:
A = 5000 * e0.1
A = 5000 * 1.105170918
A = $5525.85.
After 5 years, you would have approximately $5525.85 in the account.