A financial analyst tells you that investing in stocks will allow you to triple your money in 15 years. What annual rate of return is the analyst assuming you can earn?
(1+i)^15 = 3
log both sides
log((1+i)^15) = log3
15 log (1+i) = log3
log 1+i = log3/15
1+i = 1.07598
i = .07598
You would have to earn about 7.6 % a year to triple your money in 15 years
To determine the annual rate of return assumed by the financial analyst, we can use the compound interest formula:
Future Value = Present Value * (1 + Rate)^Time
Where:
Future Value = Tripled amount of money (3 times the initial investment)
Present Value = Initial investment
Rate = Annual rate of return (what we need to find)
Time = Number of years (15 years)
We can rearrange the formula to solve for the rate:
Rate = (Future Value / Present Value)^(1 / Time) - 1
Substituting the given values:
Rate = (3 / 1)^(1 / 15) - 1
Now, let's calculate the rate of return using these steps:
Step 1: Raise the ratio (3 / 1) to the power of (1 / 15).
Step 2: Subtract 1 from the result.
Step 3: Convert the result to a percentage.
Calculating the rate step by step:
Step 1: (3 / 1)^(1 / 15) = 1.0905 (rounded to 4 decimal places)
Step 2: 1.0905 - 1 = 0.0905
Step 3: 0.0905 * 100 = 9.05%
Therefore, the financial analyst assumes an annual rate of return of approximately 9.05%.