At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in six years, assuming interest is compounded annually?

A=PR^6 (calculate future value from present value P)

R^6=A/P=3 (triple)
R=3^(1/6) (sixth root of 3)

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To determine the rate at which you would need to invest a lump-sum amount today in order for it to triple in six years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A is the future value of the investment (in this case, triple the initial amount)
P is the principal or initial investment amount
r is the annual interest rate (unknown)
n is the number of times interest is compounded per year (annually in this case)
t is the number of years

In your scenario, you want the investment to triple, so the future value (A) is three times the initial amount (P). We can plug in the known values:

3P = P(1 + r/1)^(1 * 6)

Simplifying the equation, we are left with:

3 = (1 + r)^(6)

To solve for the unknown interest rate (r), we can take the sixth root of both sides:

(1 + r) = 3^(1/6)

(1 + r) ≈ 1.221

Subtracting 1 from both sides:

r ≈ 1.221 - 1

r ≈ 0.221

Therefore, you would need to invest at an approximate annual interest rate of 0.221 (or 22.1%) to triple your initial amount in six years, assuming interest is compounded annually.