An insurance company wants to increase sales by 15% and customer retention by 10% within...

The question asks about the time required to achieve the desired sales and retention goals, given the current rate of increase. To answer this question, we need to use the formula for compound growth rate, which is:

Final value = Initial value x (1 + Growth rate) ^ Number of periods

We can apply this formula to both sales and retention, using the given values and solving for the number of periods. For sales, we have:

1.15 = 1 x (1 + 0.06) ^ Number of periods

Taking the natural logarithm of both sides, we get:

ln(1.15) = ln(1 + 0.06) x Number of periods

Dividing by ln(1 + 0.06), we get:

Number of periods = ln(1.15) / ln(1 + 0.06)

Using a calculator, we get:

Number of periods = 2.29

Since each period is six months, we multiply by 6 to get the number of months:

Number of months = 2.29 x 6

Number of months = 13.74

Rounding up to the nearest whole number, we get:

Number of months = 14

Therefore, it will take 14 months, or about 18 months, to achieve the sales goal.

For retention, we have:

1.1 = 1 x (1 + 0.05) ^ Number of periods

Repeating the same steps as above, we get:

Number of periods = ln(1.1) / ln(1 + 0.05)

Number of periods = 1.86

Number of months = 1.86 x 6

Number of months = 11.16

Rounding up to the nearest whole number, we get:

Number of months = 12

Therefore, it will take 12 months, or 1 year, to achieve the retention goal.

References:

CBAP / CCBA Certified Business Analysis Study Guide, 2nd Edition, Chapter 5: Solution Assessment and Validation, p. 211-212

Certified Business Analysis Professional™ (CBAP®) Specialization, Course 4: Business Analysis: Solution Evaluation, Week 2: Solution Performance Assessment, Video: Solution Performance Metrics

Compound Growth Rate Calculator