SQL Server 2012 - Common Table Expression (CTE) returning more rows than it should

Question

CTE SQLFiddle

I have one lifetable with 121 rows and 3 columns (age, male and female). I have to fetch all the 121 rows considering the gender. If the gender is "Male" I fetch the column "Male" from lifetable as qx and the column "Female" as qy and vice-versa.

However, I need to calculate a fourth column, vx, whose value starts with 1 and the subsequent values are calculated as follows, using the previous value of vx itself:

vx = (vx / (1 - @interestRate)^age)

The age always goes from 0 to 120, incremented by one each step.

I am not well versed with CTEs, therefore, I'm taking baby steps to accomplish my tasks with this new method to me. and I need help.

When I try to calculate vx, the query returns 7381 instead of 121.

Here is my CTE:

DECLARE @gender VARCHAR(10) = 'MALE'
DECLARE @interestRate NUMERIC(7, 5) = 0.0354

;WITH cte AS (
    SELECT
        lt.Age,
        CASE
            WHEN @gender = 'MALE' THEN
                lt.Male
            ELSE
                lt.Female
        END AS qx,
        CASE
            WHEN @gender = 'MALE' THEN
                lt.Female
            ELSE
                lt.Male
        END AS qy,
        CAST(1.0 AS NUMERIC(7, 5)) AS vx
    FROM LifeTable AS lt

    UNION ALL

    SELECT
        cte.Age + 1,
        cte.qx,
        cte.qy,
        CAST((vx / (1 + @interestRate)) AS NUMERIC(7, 5)) AS vx
    FROM cte

    WHERE cte.Age < 120

) SELECT COUNT(*) AS NumberOfRows FROM cte OPTION (MAXRECURSION 0);

I am a little bit tired for I spent my afternoon trying to solve this, it's already night, so my question might be taken as low effort, but I really need your help to see where I am making mistakes.

Answer 1

Your problem is the anchor in the CTE returns all 120 rows instead of a single anchor row. Try this code instead, notice the WHERE clause in the CTE SELECT:

DECLARE @gender VARCHAR(10) = 'MALE'
DECLARE @interestRate NUMERIC(7, 5) = 0.0354

;WITH cte AS (
    SELECT
        lt.Age,
        CASE
            WHEN @gender = 'MALE' THEN
                lt.Male
            ELSE
                lt.Female
        END AS qx,
        CASE
            WHEN @gender = 'MALE' THEN
                lt.Female
            ELSE
                lt.Male
        END AS qy,
        CAST(1.0 AS NUMERIC(7, 5)) AS vx
    FROM LifeTable AS lt
    WHERE Age = 1
    UNION ALL

    SELECT
        cte.Age + 1,
        cte.qx,
        cte.qy,
        CAST((vx / (1 + @interestRate)) AS NUMERIC(7, 5)) AS vx
    FROM cte

    WHERE cte.Age < 120

) SELECT COUNT(*) AS NumberOfRows FROM cte OPTION (MAXRECURSION 0);