Calculate value based on value from same column of the previous row - sql-server

Question

I have an issue where I have to calculate a column using a formula that uses the value from the calculation done in the previous row.
I have tried the lag function but cannot get past the 2nd row. After that all my values are null, since that column originally starts as null. I feel like I am missing something.
I need to calculate a new column, using the formula:
MovingRate = MonthlyRate + (0.7 * MovingRatePrevious)
... where the MovingRatePrevious is the MovingRate of the prior row. For month 1, I have the value so I do not need to re-calculate that but I need that value to be able to calculate the subsequent rows. I need to partition by Type.
This is my original dataset:
Month Type MonthyRate MovingRate
--------------------------------------
1 Blue 0.400 0.330
2 Blue 0.300
3 Blue 0.700
4 Blue 0.900
Desired results in MovingRate column:
Month Type MonthyRate MovingRate
---------------------------------------
1 Blue 0.400 0.330
2 Blue 0.300 0.531
3 Blue 0.700 1.072
4 Blue 0.900 1.650

Answer 1

You can calculate it using recursive CTE. Below is a generalized version for your data:
DECLARE #t TABLE (Month INT, Type VARCHAR(100), MonthlyRate DECIMAL(18, 3));
INSERT INTO #t VALUES
(1, 'Blue', 0.400),
(2, 'Blue', 0.300),
(3, 'Blue', 0.700),
(4, 'Blue', 0.900);
WITH cte1 AS (
SELECT *, ROW_NUMBER() OVER (PARTITION BY Type ORDER BY Month) AS rn
FROM #t
), rcte AS (
SELECT *, CAST(0.330 AS DECIMAL(18, 3)) AS MovingRate
FROM cte1 AS base
WHERE rn = 1
UNION ALL
SELECT curr.*, CAST(curr.MonthlyRate + 0.7 * prev.MovingRate AS DECIMAL(18, 3))
FROM cte1 AS curr
JOIN rcte AS prev ON curr.Type = prev.type AND curr.rn = prev.rn + 1
)
SELECT *
FROM rcte