question 32 points 2 if you put money into a compound interest account with a 7.2% interest rate, how many…

Explanation:

Step1: Recall 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 (in decimal form), and $t$ is the number of years. We want to double our money, so $A = 2P$, and $r=0.072$. Substituting these values into the formula gives $2P=P(1 + 0.072)^t$.

Step2: Simplify the equation

Divide both sides of the equation $2P=P(1 + 0.072)^t$ by $P$ (since $P\neq0$), we get $2=(1.072)^t$.

Step3: Take the natural logarithm of both sides

$\ln(2)=\ln(1.072^t)$. Using the property of logarithms $\ln(a^b)=b\ln(a)$, we can rewrite the right - hand side as $t\ln(1.072)$. So, $\ln(2)=t\ln(1.072)$.

Step4: Solve for $t$

$t=\frac{\ln(2)}{\ln(1.072)}$. We know that $\ln(2)\approx0.693$ and $\ln(1.072)\approx0.0695$. Then $t=\frac{0.693}{0.0695}\approx10$.

Answer:

10 years