17.Elegant Designers have generated sales of $625,000 for the current year. If they can grow their sales at a rate of 12 percent every year, how long will they take to triple their sales?
10
To find out how long it will take for Elegant Designers to triple their sales, we need to use the compound interest formula since the sales are growing at a constant rate. The compound interest formula is:
Final Value = Initial Value * (1 + Growth Rate)^Time
In this case, the final value is three times the initial value, so we have:
3 * $625,000 = $625,000 * (1 + 0.12)^Time
Divide both sides by $625,000 to isolate the exponential term:
3 = (1 + 0.12)^Time
Take the natural logarithm of both sides to bring down the exponent:
ln(3) = ln((1 + 0.12)^Time)
Since ln((1 + 0.12)^Time) can be simplified to Time * ln(1 + 0.12), we have:
ln(3) = Time * ln(1 + 0.12)
Now, divide both sides by ln(1 + 0.12) to solve for Time:
Time = ln(3) / ln(1 + 0.12)
Using a calculator, we find:
Time ≈ 9.73 years
Therefore, it will take Elegant Designers approximately 9.73 years to triple their sales if they grow their sales at a rate of 12 percent every year.