Question

Suppose an investment offers to quintuple your money in 24 months (don’t believe it). What rate of return per quarter are you being offered? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Rate of return

Answer 1

To find the rate of return per quarter for an investment that quintuples in 24 months, use the future value formula with periodic compounding; the calculation yields approximately 18.17% per quarter.

Step-by-step explanation:

To find the rate of return per quarter for an investment that quintuples money in 24 months, we need to use the formula for the future value of an investment compounded periodically:

FV = PV * (1 + r)^n

Where:

• FV is the future value of the investment
• PV is the present value of the investment
• r is the periodic rate of return
• n is the number of periods

If the investment quintuples, the FV is 5 times the PV. Since we are looking for the rate per quarter, and there are 24 months, that makes 24 / 3 = 8 quarters. Let's denote 'r' as our unknown quarterly rate of return and solve for 'r':

5 = (1 + r)^8

We can now solve for 'r' using algebra:

r = (5^(1/8)) - 1

Calculating the value, we get the quarterly rate of return as follows:

r ≈ 0.18169 or 18.17% per quarter when rounded to two decimal places.

Answer 2

To find the quarterly rate of return for an investment that quintuples your money in 24 months, you would use the compound interest formula and solve for the annual interest rate before dividing by 4 to find the quarterly rate.

Step-by-step explanation:

If an investment promises to quintuple your money in 24 months, we need to determine the equivalent quarterly rate of return. Since there are 8 quarters in 24 months, we can represent this scenario using the compound interest formula:
A = P(1 + r/n)^(nt)

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested or borrowed for, in years.

In your scenario, A/P should be equal to 5, as the money quintuples, n is 4 (as compounding occurs quarterly), and t is 2 years (which is 24 months).

The formula then becomes:

5 = (1 + r/4)^(4*2)

After solving for r, you would get:

r = 4*((5^(1/8)) - 1)

So, r is approximately 152.00% (rounded to two decimal places).