Answer:
The president of the bank needs an annual interest rate of approximately 5.36% compounded annually to grow his investment portfolio from $18 million to $25 million in 8 years.
Explanation:
To find the interest rate compounded annually, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = final amount ($25 million)
P = initial amount ($18 million)
r = interest rate (what we're trying to find)
n = number of times interest is compounded per year (annually)
t = time in years (8 years)
Substituting the given values, we get:
$25 million = $18 million(1 + r/1)^(1*8)
Simplifying the equation, we get:
(25/18) = (1 + r)^8
Taking the eighth root of both sides, we get:
(25/18)^(1/8) = 1 + r
Subtracting 1 from both sides, we get:
r = (25/18)^(1/8) - 1
Using a calculator, we get:
r ≈ 0.0536 or 5.36%