Final answer:
To calculate the balance after 5 years with continuous compounding interest, use the formula A = Pe^(rt). The final balance with a $6000 deposit at 7% interest compounded continuously for 5 years is $8514.41.
Step-by-step explanation:
To find out how much you will have in an account after 5 years with continuous compounding interest, you can use the formula A = Pert, where:
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- t is the time in years
- e is the base of the natural logarithm (approximately equal to 2.71828)
In this case, you deposit $6000 at 7% interest compounded continuously for 5 years. Converting the interest rate to decimal form gives us 0.07. Using the formula:
A = 6000e0.07 × 5
Now, calculate the value of e raised to the power of 0.07 multiplied by 5:
A = 6000 × e0.35
Using a calculator, we find:
A = 6000 × 1.4190675
A = $8514.41 (rounded to two decimal places)
After 5 years, with continuous compounding, the balance in the account will be $8514.41.