Question

The president of a bank has $18 million in his banks investment portfolio that he wants to grow to $25 million in 8 years. What interest rate compounded annually does he need for this investment

Answer 1

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%