Use the model $A=P e^{r t}$ or $A=P\left(1+\frac{r}{n}\right)^{n t}$, where $A$ is the future value of $P$ dollars invested at interest rate $r$ compounded continuously or $n$ times per year for $t$ years. If a couple has $\$ 100,000$ in a retirement account, how long will it take the money to grow to $\$ 1,000,000$ if it grows by $6.5 \%$ compounded continuously? Round up to the nearest year. It will take approximately years. \[ \times \] 5

Step 1 ：We are given the initial amount (P) as $100,000, the final amount (A) as $1,000,000, and the interest rate (r) as $6.5\%$ or $0.065$ in decimal form. We are asked to find the time (t) it will take for the initial amount to grow to the final amount. We can use the formula for continuous compounding $A=P e^{r t}$ and solve for t.

Step 2 ：Substitute the given values into the formula: $1,000,000 = 100,000 \times e^{0.065 \times t}$

Step 3 ：Solve the equation for t, we get t approximately equals to 36

Step 4 ：Final Answer: It will take approximately \(\boxed{36}\) years for the money to grow to $1,000,000.