You can calculate membership retention rate by building two queries and performing this calculation to get a percentage: 
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Step 1: Create a Selection of 1st Year Members 
First, we need to isolate the first year members we'd like to include in our reporting. In this example, we will view a query of everyone who joined as a member in 2015.
  1. Go to Analysis > Information Library 
  2. Click Add an ad-hoc query 
  3. Select the source view of Memberships and click OK.
  4. From the left column, highlight the Membership Transaction Node. From the middle column, drag Action to Include Records Where. Set this to be equal to Join. Your field should appear like this: Membership Transaction\Action is equal to Join
  5. From the middle column, drag Transaction date (date only) to Include Records Where. Set this to be equal to the date range you're looking to analyze. In this example: Membership Transaction\Transaction date (date only) is between 1/1/15 and 12/31/15. Your query will look similar to this one:                            User-added image
  6. Click Preview Results. Make note of the number of records in the results. This will be the # of New Members in the calculation above. In this example, we had 110 new members in 2015:   User-added image
  7. On the Set Save Options tab, name your query and check the boxes to Create a selection and to Show this Selection in the Query Designer:                                                                  User-added image
  8. Click Save and Close 
Step 2: Create a selection to see which members renewed
Next, we will create a query to see which members from this group renewed the following year. This will give us the # of New Members who renewed in the calculation above. 
  1. Go to Analysis > Information Library 
  2. Click Add an ad-hoc query 
  3. Select the source view of Memberships and click OK. 
  4. From the left column, highlight the Selections Folder. In the middle column, double click the name of the query you saved in Step 1. You should see an Apply criteria window pop up. Set this criteria to be equal to Yes and click OK. Your field should appear like this: Exists in "Query Name (Ad-hoc Query)" is equal to Yes. This will pull in the previous group of members who joined as members for the first time in 2015:                                                              User-added image
  5. From the left column, highlight the Membership Transaction Node. From the middle column, drag Action to Include Records Where. Set this to be equal to Join. Your field should appear like this: Membership Transaction\Action is one of Renew, Upgrade, Downgrade, or Rejoin. 
  6. From the middle column, drag Transaction date (date only) to Include Records Where. Set this to be equal to the date range your new members would have renewed during. In this example: Membership Transaction\Transaction date (date only) is between 1/1/16 and 12/31/16. Your query will look similar to this one:  User-added image                          
  7. Click Preview Results. Make note of the number of records in the results. This will be the # of New Members in the calculation above. In this example, we 33 of our new members renewed:  User-added image 
  8. Complete the calculation above, using this number as the # of New Members Who Renewed. In our example 33/100 X 100 = 33%. Our new member retention rate is 33%. 
Note: Another option if you'd like to do some additional analysis around first year member retention in addition to a simple calculation (for example, break the member retention rate down by level or see how long after their expiration date they renewed), another option would be to use the Query from Step 1 to create an export process to export membership transaction history (their join transaction and their subsequent renewal transactions). Our related solution will instruct you how to build an export process: I need to find last membership transaction date to see when members renew