Final answer:
To determine Frank's annual rate of return on his investment over 5 years, the compound interest formula is applied, leading to the calculation of the 5th root of 5 minus 1 after determining that the investment amount was increased by 5 times.
Step-by-step explanation:
To answer the question of what annual rate of return Frank earned on his investment when he increased his initial $10,000 investment by 5 times over 5 years, we will need to use the formula for compound interest:
Principal(1 + rate)time = Amount
Since Frank's investment increased by 5 times, the final amount is $10,000 * 5 = $50,000. Plugging the values into the formula, we get:
10000(1 + rate)^5 = 50000
To find the rate, we need to solve for rate:
- (1 + rate)^5 = 50000 / 10000
- (1 + rate)^5 = 5
- 1 + rate = the 5th root of 5
- rate = the 5th root of 5 - 1
After calculating the 5th root of 5 and subtracting 1, we determine the annual rate of return.