you invest $6500 into a mutual fund that is expected to earn 6% per year. how long will it take the fund to…

Explanation:

Step1: Identify 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. Here, $P=$6500$, $A = $13000$, and $r=0.06$.

Step2: Substitute values into formula

Substitute the values into the formula: $13000=6500(1 + 0.06)^t$.

Step3: Simplify the equation

Divide both sides of the equation by $6500$: $\frac{13000}{6500}=(1.06)^t$, which simplifies to $2=(1.06)^t$.

Step4: Take the natural logarithm of both sides

$\ln(2)=\ln(1.06^t)$. Using the property of logarithms $\ln(a^b)=b\ln(a)$, we get $\ln(2)=t\ln(1.06)$.

Step5: Solve for $t$

$t=\frac{\ln(2)}{\ln(1.06)}$. Calculate $\ln(2)\approx0.6931$ and $\ln(1.06)\approx0.0583$. Then $t=\frac{0.6931}{0.0583}\approx12$.

Answer:

C. 12 years