Question

Apply the formula A=Pe^rt
, 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

aswer in 5 steps only using numbers

Answer 2

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 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**.