(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
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
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%.