The interest rate r required to increase investment p to amount a in t years is found using the formula r=(a/p)^1-t - 1. Find the interest rate r when p =2500, a =3600, and t =2.

The interest rate would be 20%.

The formula is derived from the compound interest formula

[tex]A=p(1+r)^t[/tex].

We want to isolate r in this equation to rewrite the formula.  The first thing we would cancel, outside parentheses, would be p; divide both sides by p and we have

[tex]\frac{A}{p}=(1+r)^t[/tex]

We want to cancel the exponent, t, next.  We can raise a power to its reciprocal to undo it; for example, raising a squared amount to the 1/2 power will undo the exponent.  We will raise both sides of this to the 1/t power:

[tex](\frac{A}{p})^{\frac{1}{t}}=1+r[/tex]

Now we cancel the 1 by subtracting, giving us

[tex](\frac{A}{p})^{\frac{1}{t}}-1=r[/tex]

Using this formula, we plug in 3600 for A, 2500 for p and 2 for t: