We can use the compound interest formula to find the annual rate of return on the account:
A = P(1 + r/n)^(nt)
where:
A = final amount = $40,000
P = principal amount = $400
r = annual interest rate (unknown)
n = number of times interest is compounded per year (unknown)
t = time in years = 44
We can simplify the formula by noting that interest was likely compounded annually (n = 1), so we have:
A = P(1 + r)^t
Taking the ratio of the final amount to the principal amount, we get:
A/P = (1 + r)^t
Substituting in the values we know, we get:
40,000 / 400 = (1 + r)^44
Simplifying the left side, we get:
100 = (1 + r)^44
Taking the 44th root of both sides, we get:
1 + r = 1.0663
Subtracting 1 from both sides, we get:
r = 0.0663 = 6.63%
Answer:
Therefore, the annual rate of return on the account was approximately 6.63%.