Apply the formula  A=Pert , 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) explain in 3 sentences

1 answer

To calculate the amount accrued from Dora's investment using the formula \( A = Pe^{rt} \), we start by identifying the values: \( P = 5000 \), \( r = 0.025 \) (which is 2.5% expressed as a decimal), and \( t = 10 \). Next, we plug in these values into the formula:

\[ A = 5000 \cdot e^{(0.025 \cdot 10)} = 5000 \cdot e^{0.25} \]

Using a calculator, we find \( e^{0.25} \) to be approximately 1.2840, so then we calculate:

\[ A \approx 5000 \cdot 1.2840 \approx 6420 \]

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