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Each year Capital Two retains 75 percent of its customers, and the annual discount rate is 5 percent. What annual retention rate doubles the value of a customer?

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Answer:  87.5%

Explanation:

Value of a Customer = Margin * Retention rate / (1 + Annual discount rate - Retention rate)

We shall assume a margin of 1 so no need to include it:

= 75% / ( 1 + 5% - 75%)

= 2.5

This value needs to double so assume the retention rate to double this is x and use the formula above to find it:

5 = x / (1 + 5% - x)

5 *  (1 + 5% - x) = x

5 + 0.25 - 5x = x

5.25 = 5x+ x

6x = 5.25

x = 5.25 / 6

x = 87.5%

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