How much money, invested at an interest rate of r % per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.)
A = 15,000, r = 4.5, t = 4
I know that A=Pe^rt but I keep getting the wrong answer
NEVERMIND. I just kept making a calculator entry error.
To solve this problem, you are correct in using the formula A = Pe^rt. However, it seems like you might be making a mistake while plugging in the values. Let's go through the steps together:
Step 1: Identify the given values:
A = $15,000 (target amount)
r = 4.5% (interest rate, but remember to express it in decimal form)
t = 4 years
Step 2: Convert the interest rate to decimal form:
r = 4.5% = 0.045
Step 3: Plug the values into the formula A = Pe^rt:
A = P * e^(r * t)
Step 4: Rearrange the equation to solve for P:
Divide both sides of the equation by e^(r * t):
A / e^(r * t) = P
Step 5: Substitute the given values and calculate P:
P = $15,000 / e^(0.045 * 4)
Step 6: Use a calculator to evaluate the exponent and round the answer to the nearest cent:
P ≈ $12,487.78 (rounded to the nearest cent)
So, if you invest approximately $12,487.78 at an interest rate of 4.5% per year compounded continuously for 4 years, it will amount to $15,000.