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:
\(21000 = 15000(1 + 0.15/1) ^{1*t} \\ 21000=15000(1+0.15) ^{t} \\ 21000 = 15000 * 1.15 ^{t} \\ 1.15 ^{t}=21000/15000 \\ 1.15 ^{t}=1.4\)
Now, logarithm both sides of the equation:
\(log(1.15 ^{t})=log(1.4)\)
Since \(log (x^{a}) =a*log(x)\), then \(log (1.15^{t}) =t*log(1.15)\)
Therefore:
\(t*log(1.15)=log(1.4) \\
t = \frac{log(1.4)}{log(1.15)} \\
t = \frac{0.15}{0.06} \\
t = 2.5\)
