Suppose an investment offers to double your money in 12 months. What rate of return per quarter are you being offered?
let quarterly rate be i
1(1+i)^4 = 2
1+i = 2^(1/4)
1+i = 1.189207
i = .189207
annual rate compounded quarterly is
.7568 or 75.68%
(I want in !)
To determine the rate of return per quarter, we need to divide the annual rate of return by the number of quarters in a year.
1. Start with the annual rate of return, which is to double the money in 12 months. This means you will receive a 100% return on your investment in a year.
2. Divide the annual rate of return by the number of quarters in a year. Since there are four quarters in a year, divide 100% by 4:
100% / 4 = 25%
Therefore, you are being offered a 25% rate of return per quarter.
To determine the rate of return per quarter, we need to calculate the compound interest rate per quarter that would result in doubling the investment in 12 months. Here's how you can do that:
1. Start with the initial investment amount (let's assume it's $1).
2. Divide the final amount (in this case, $2) by the initial amount to get the growth factor: 2/1 = 2.
3. Take the 12th root of the growth factor to get the quarterly growth factor since there are 12 months in a year: ∛2.
4. Subtract 1 from the quarterly growth factor to get the rate of return per quarter.
5. Multiply the result by 100 to express it as a percentage.
Let's perform the calculation:
Quarterly Growth Factor = ∛2 ≈ 1.0905077
Rate of Return per Quarter = 1.0905077 - 1 ≈ 0.0905077
Rate of Return per Quarter (as a percentage) = 0.0905077 × 100 ≈ 9.05%
So, you are being offered a rate of return of approximately 9.05% per quarter in this investment.