Suppose that any given year, the value of a certain investment is increased by 15%. if the value is now $15,000, in how many years will the value be $21,000?

The answer is 2.5 years.

The compound interest formula is:
A = P(1 + r/n)ⁿˣ
A - the final value
P - the initial value
r - the interest rate
n - the number of times interest is compounded by year
t - the numbers of years of investment

We have:
A = $21,000
P = $15,000
r = 15% = 15/100 = 0.15
n = 1       (since this is per year)
t = ?

So:


Now, logarithm both sides of the equation:


Since , then
Therefore:

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