Apply the formula A=Pe^rt

Question

, where A
is the amount accrued, P
is the principal, r is the rate of interest, and t is the time, in years. Dora invests $5,000 in an account that is compounded continuously at an annual interest rate of 2.5%. In 10 years, how much will Dora’s investment be worth to the nearest dollar? Show the steps that Dora must take to solve this problem.(4 points)

Answer 1

To calculate the amount accrued using the formula \( A = Pe^{rt} \), follow these steps:

Given Data:

• Principal (\( P \)) = $5,000
• Annual interest rate (\( r \)) = 2.5% = 0.025 (as a decimal)
• Time (\( t \)) = 10 years

Step 1: Write the formula

The formula to calculate the amount accrued is: \[ A = Pe^{rt} \]

Step 2: Substitute the values into the formula

Now, substitute \( P \), \( r \), and \( t \) into the formula: \[ A = 5000 \times e^{(0.025 \times 10)} \]

Step 3: Calculate \( rt \)

First, calculate \( rt \): \[ rt = 0.025 \times 10 = 0.25 \]

Step 4: Calculate \( e^{rt} \)

Next, calculate \( e^{0.25} \). You can use a scientific calculator or an online calculator for this: \[ e^{0.25} \approx 1.284025 \]

Step 5: Calculate \( A \)

Now plug \( e^{rt} \) back into the equation: \[ A = 5000 \times 1.284025 \] \[ A \approx 6420.125 \]

Step 6: Round to the nearest dollar

Finally, round the amount to the nearest dollar: \[ A \approx 6420 \]

Conclusion

Dora’s investment will be worth approximately $6,420 in 10 years.

Answer 2

aswer in 5 steps only using numbers

Answer 3

Sure! Here are the steps just using numbers:

1. Given Values:
   \( P = 5000 \)
   \( r = 0.025 \)
   \( t = 10 \)

2. Calculate \( rt \):
   \( rt = 0.025 \times 10 = 0.25 \)

3. Calculate \( e^{rt} \):
   \( e^{0.25} \approx 1.284025 \)

4. Calculate \( A \):
   \( A = 5000 \times 1.284025 \approx 6420.125 \)

5. Round to Nearest Dollar:
   \( A \approx 6420 \)

Dora's investment will be worth $6,420.