You purchase a piece of property for $30,000 nine years ago and sold it today for $83,190. What was your annual rate of return on your investment?
P = Po(1+r)^n = 83,190.
r = APR expressed as a decimal.
n = The number of compounding periods.
30,000(1+r)^9 = 83,190.
(1+r)^9 = 83,190/30,000 = 2.773,
9*Log(1+r) = Log2.773,
Log(1+r) = Log2.773/9 = 0.0492,
1+r = 10^(0.0492) = 1.12,
r = 1.12-1 = 0.12 = 12%.
Well, let's see. You bought the property for $30,000 nine years ago and sold it today for $83,190. That's quite a jump! It seems like your investment did quite well. Now, to calculate your annual rate of return, we need to bring in some math. But don't worry, I won't make it as daunting as trying to calculate the value of x in those scary algebra equations.
Using a financial formula, we can determine your annual rate of return. So, if you bear with me, I'll crunch some numbers for you.
(*sound of calculators clattering*)
Alright, after some intense calculations (and a few accidental button presses that made weird noises), it appears that your annual rate of return on the investment is approximately 13.26%. Now, that may not sound as exciting as a roller coaster ride, but hey, a profit is a profit, right? Congratulations on your successful investment!
Remember, though, this is just a ballpark figure. Factors like taxes, fees, and other expenses may affect the actual rate. So take this number with a grain of clown-nose-shaped salt!
To calculate the annual rate of return on your investment, you need to use the formula for compound annual growth rate (CAGR):
CAGR = ((Ending Value / Beginning Value)^(1 / Number of Years)) - 1
In this case, the beginning value is $30,000, the ending value is $83,190, and the number of years is 9.
CAGR = (($83,190 / $30,000)^(1 / 9)) - 1
CAGR ≈ (2.773^0.111) - 1
CAGR ≈ (1.073) - 1
CAGR ≈ 0.073
To express the annual rate of return as a percentage, multiply the result by 100:
Annual Rate of Return ≈ 0.073 * 100
Annual Rate of Return ≈ 7.3%
Therefore, your annual rate of return on your investment is approximately 7.3%.
To calculate the annual rate of return on your investment, you need to use the formula:
Annual Rate of Return = (Ending Value / Beginning Value)^(1 / Number of Years) - 1
Let's plug the given values into the formula:
Beginning Value = $30,000
Ending Value = $83,190
Number of Years = 9
Annual Rate of Return = ($83,190 / $30,000)^(1 / 9) - 1
Now, let's solve it step by step:
Step 1: Divide the Ending Value by the Beginning Value:
$83,190 / $30,000 = 2.773
Step 2: Calculate the exponent value, 1 divided by the Number of Years:
1 / 9 = 0.111
Step 3: Raise the result from Step 1 to the power of the result from Step 2:
2.773^0.111 ≈ 1.084
Step 4: Subtract 1 from the result obtained in Step 3:
1.084 - 1 = 0.084
The annual rate of return on your investment is approximately 8.4%.