Question

Aaliyah is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Aaliyah need to invest, to the nearest hundred dollars, for the value of the account to reach $181,000 in 19 years?

Answer 1

Aaliyah needs to invest approximately $78,207 to have a value of $181,000 in 19 years in an account paying an interest rate of 5% compounded continuously.

Step-by-step explanation:

To find out how much Aaliyah needs to invest, we can use the continuous compound interest formula:

A = P * e^(rt)

where A is the future value, P is the principal amount invested, r is the annual interest rate, and t is the time in years. We are given that A = $181,000, r = 0.05, and t = 19. Let's solve for P:

$181,000 = P * e^(0.05 * 19)

P = $181,000 / e^(0.05 * 19)

Using a calculator, the value of P rounds to the nearest hundred dollars is approximately $78,207.