Question

3. The formula A = Pet is used when dealing with

continuously compounded interest, where A = accumulated
money, P = beginning principle of money, r = rate of
interest (as a decimal), and t = time in years. How much
money would Paul have in the bank at 6.5% interest
compounded continuously, after 8 years, if his initial
deposit was $4,000. Round to the nearest penny.

Answer 1

To calculate the accumulated amount with continuously compounded interest, the formula A = Pe^(rt) is used. For Paul with a $4,000 initial deposit at a 6.5% interest rate over 8 years, the final amount is approximately $7,226.20.

Step-by-step explanation:

To calculate how much money Paul would have in the bank after 8 years at a 6.5% interest rate compounded continuously, we use the formula for continuously compounded interest: A = Pert, where A is the accumulated money, P is the principal amount, r is the interest rate as a decimal, and t is the time in years.

In this case, Paul's initial deposit (the principal P) is $4,000, the interest rate (r) is 6.5%, which as a decimal is 0.065, and the time (t) is 8 years.

The formula becomes: A = $4,000 × e0.065 × 8.

Using a calculator that has an e (exponential) function, we calculate: A ≈ $4,000 × e0.52 which gives us the total accumulated amount.

Paul will have approximately $7,226.20 in the bank after 8 years, rounded to the nearest penny.