in its first 10 years a mutual fund produced an average annual return of 19.23%. assume that money invested…

in its first 10 years a mutual fund produced an average annual return of 19.23%. assume that money invested in this fund continues to earn 19.23% compounded annually. how long will it take money invested in this fund to double? it will take approximately year(s) for the money invested in this fund to double. (round up to the nearest year.)

Answer

Explanation:

Step1: Use compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. We want to find the time $t$ when $A = 2P$ and $r=0.1923$. Substitute $A = 2P$ into the formula: $2P=P(1 + 0.1923)^t$.

Step2: Simplify the equation

Divide both sides of the equation $2P=P(1 + 0.1923)^t$ by $P$ (since $P\neq0$). We get $2=(1.1923)^t$.

Step3: Take the natural logarithm of both sides

$\ln(2)=\ln(1.1923^t)$. Using the property of logarithms $\ln(a^b)=b\ln(a)$, we have $\ln(2)=t\ln(1.1923)$.

Step4: Solve for $t$

$t=\frac{\ln(2)}{\ln(1.1923)}$. Calculate $\ln(2)\approx0.6931$ and $\ln(1.1923)\approx0.176$. Then $t=\frac{0.6931}{0.176}\approx3.94$.