Final answer:
To find the annual rate of return that increased Frank's investment by three times in nine years, we use the compound interest formula. Frank's initial investment of $10,000 turned into $30,000 in nine years. Solving the compound interest equation yields the annual rate of return.
Step-by-step explanation:
The student is asking about the annual rate of return on an investment that grew threefold over nine years. To solve this, we need to use the formula for compound interest, which is A = P(1 + r)n, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), and n is the number of years the money is invested.
Frank's investment increased by 3 times over 9 years. If he initially invested $10,000, his investment grew to $30,000. Plugging the values into the formula and solving for r, we get:
30,000 = 10,000(1+r)9
Dividing both sides by 10,000 gives us:
3 = (1+r)9
By taking the ninth root of both sides of the equation and then subtracting 1, we find the annual rate of return r that Frank earned.