Firstly, to calculate the continuously compounded interest, we use the formula A=Pe^(rt).
Here:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (in decimal).
t is the time the money is invested for in years.
Given:
P = $550,000 which is the initial investment (principal amount).
r = 1 +(1/8) i.e, 1.125 in decimal format.
t = 6 years.
Substituting the values into the formula,
A = $550,000 * e^(1.125 * 6)
When we subtract the principal from the total amount, we get the interest earned on the principal. i.e,
Interest = A - P = $550,000 * e^(1.125 * 6) - $550,000
After calculating, the interest amount is found to be approximately $469,182,319.3893834.
And if rounded to the nearest cent, we get approximately $469,182,319.39.
Hence, the interest earned on a $550,000 deposited for six years at 1(1)/(8)% interest compounded continuously, is approximately $469,182,319.39.