Isabella invests $10,000 in an account that is compounded continuously at an annual interest rate of 3%, according to 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. Apply the formula to find out how much Isabella’s investment will be worth in 15 years, to the nearest dollar.(1 point)
The formula A=Pe^rt can be used to find the amount accrued after 15 years:
A = P * e^(r*t)
In this case, P = $10,000, r = 0.03, and t = 15 years.
A = 10000 * e^(0.03*15)
Now we can calculate the value of the expression e^(0.03*15):
e^(0.03*15) ≈ 1.532417
So, the amount accrued after 15 years is approximately:
A ≈ 10000 * 1.532417
A ≈ $15,324.17
Therefore, Isabella's investment will be worth approximately $15,324.17 in 15 years.