Suppose an investment offers to triple your money in 12 months (don’t believe it). What rate of return per quarter are you being offered?
p * (x)^4 = 3 p
(x)^4 = 3
x = 1.316
so .316 per quarter = 31.6% per quarter
To determine the rate of return per quarter, we can use the compound interest formula:
Future Value (FV) = Present Value (PV) * (1 + r)^n
Where:
- FV is the future value
- PV is the present value
- r is the rate of return per period (in this case, per quarter)
- n is the number of periods (in this case, quarters)
In this scenario, let's assume that you invest an amount of $1. To triple your money, the future value (FV) would be $3.
Therefore, we can rewrite the formula as:
3 = 1 * (1 + r)^n
To solve for the rate of return per quarter (r), we need to isolate "r" in the equation. Taking the natural logarithm (ln) of both sides of the equation can help us with this.
ln(3) = ln(1 + r)^n
Applying the logarithmic property, we can multiply the exponent "n" to the logarithm:
ln(3) = n * ln(1 + r)
Now, let's solve for the rate of return per quarter (r). Divide both sides of the equation by "n":
ln(3) / n = ln(1 + r)
Next, raise the constant term (e) to the power of both sides of the equation:
e^(ln(3) / n) = 1 + r
Finally, subtract 1 from both sides and get the value of the rate of return per quarter (r):
r = e^(ln(3) / n) - 1
Given that you're being offered the opportunity to triple your money in 12 months (which is equivalent to 4 quarters), let's calculate the rate of return per quarter:
r = e^(ln(3) / 4) - 1
Using a calculator or coding language, you can evaluate this expression to find the rate of return per quarter.