What will be the sales figure for the P.J.Cramer Company at the end of six years if it grows at a compound rate of 20 percent annually from $500,000?

Steps to Solve

1. Identify the variables We need the current sales figure, the growth rate, and the time period. Let's denote:

• Current Sales = $P$
• Annual Growth Rate = $r$ (as a decimal)
• Time = $t$ (in years)

2. Write the compound growth formula To calculate future sales, we will use the formula:

$$ A = P(1 + r)^t $$

Where:

• $A$ is the amount of future sales,
• $P$ is the current sales figure,
• $r$ is the annual growth rate (as a decimal),
• $t$ is the number of years.

3. Plug in the values Insert the values of $P$, $r$, and $t$ into the formula. For example, if $P = 100000$, $r = 0.05$, and $t = 6$, it would look like:

$$ A = 100000(1 + 0.05)^6 $$

4. Calculate the future sales Now we compute the value of $A$. First, calculate $1 + r$:

$$ 1 + 0.05 = 1.05 $$

Then raise it to the power of $t$:

$$ 1.05^6 $$

Finally, multiply by $P$:

$$ A = 100000 \times (1.05^6) $$

5. Finalize the calculation Using a calculator, find $1.05^6$, then multiply by the current sales figure to get the future sales amount.