How much would 500 invested at 5 percent interest compounded continuously be worth after 10 years?

To calculate the future value of an investment with continuous compounding, you can use the formula ( A = Pe^{rt} ), where ( A ) is the amount, ( P ) is the principal, ( r ) is the interest rate, and ( t ) is the time in years. For an investment of $500 at a 5% interest rate compounded continuously for 10 years, the calculation would be:

[ A = 500 \times e^{0.05 \times 10} \approx 500 \times e^{0.5} \approx 500 \times 1.6487 \approx 824.35. ]

Thus, the investment would be worth approximately $824.35 after 10 years.