Apply the formula A=Pert

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.

Answer 1

To solve the problem using the formula \( A = Pe^{rt} \), let's break it down into steps:

1. Identify the variables:

   • \( P \) (the principal) = $5,000
   • \( r \) (the annual interest rate) = 2.5% = 0.025 (as a decimal)
   • \( t \) (the time in years) = 10 years

2. Write down the formula: \[ A = Pe^{rt} \]

3. Substitute the values into the formula: \[ A = 5000 \cdot e^{(0.025 \cdot 10)} \]

4. Calculate \( rt \): \[ rt = 0.025 \cdot 10 = 0.25 \]

5. Calculate \( e^{0.25} \): Using a scientific calculator or an approximation: \[ e^{0.25} \approx 1.284025 \]

6. Substitute back into the formula: \[ A = 5000 \cdot 1.284025 \]

7. Multiply to find \( A \): \[ A \approx 5000 \cdot 1.284025 = 6420.125 \]

8. Round to the nearest dollar: \[ A \approx 6420 \]

Therefore, after 10 years, Dora's investment will be worth approximately $6,420.