At what annual rate would $200 have to be invested to grow to 497.65 in 5 years?

To solve this problem, we can use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

In this case, we know that A = $497.65, P =$200, n = 1 (since we're looking for an annual rate), and t = 5 years. We're trying to solve for r.

First, divide both sides of the equation by P to isolate the terms with r:

A/P = (1 + r/n)^(nt)

Substitute the known values:

497.65/200 = (1 + r/1)^(1*5)

2.48825 = (1 + r)^5

Take the fifth root of both sides to solve for (1 + r):

(2.48825)^(1/5) = 1 + r

1.199 = 1 + r

Subtract 1 from both sides to solve for r:

r = 1.199 - 1

r = 0.199

So, the annual interest rate would need to be approximately 0.199, or 19.9%, for $200 to grow to$497.65 in 5 years.