[mysql] MySQL - sum column value(s) based on row from the same table

I'm trying to get 'Cash', 'Check' and 'Credit Card' totals in new columns based on ProductID from the same table.

Table - Payments

+-----------+------------+---------------+--------+
| ProductID |  SaleDate  | PaymentMethod | Amount |
+-----------+------------+---------------+--------+
|         3 | 2012-02-10 | Cash          |     10 |
|         3 | 2012-02-10 | Cash          |     10 |
|         3 | 2012-02-10 | Check         |     15 |
|         3 | 2012-02-10 | Credit Card   |     25 |
|         4 | 2012-02-10 | Cash          |      5 |
|         4 | 2012-02-10 | Check         |      6 |
|         4 | 2012-02-10 | Credit Card   |      7 |
+-----------+------------+---------------+--------+

Desired Output -

+------------+------+-------+-------------+-------+
| ProductID  | Cash | Check | Credit Card | Total |
+------------+------+-------+-------------+-------+
|          3 |   20 |    15 |          25 |    60 |
|          4 |    5 |     6 |           7 |    18 |
+------------+------+-------+-------------+-------+

I've tried LEFT JOINing the same table but haven't had any success. Any suggestions would be appreciated. Thanks.

Unsuccessful and incomplete attempt -

SELECT P.ProductID, Sum( PCash.Amount ) AS 'Cash', SUM( PCheck.Amount ) AS 'Check', SUM( PCredit.Amount) AS 'Credit Card' 
FROM Payments AS P 
LEFT JOIN Payments AS PCash ON P.ProductID = PCash.ProductID AND PCash.PaymentMethod = 'Cash'
LEFT JOIN Payments AS PCheck ON P.ProductID = PCheck.ProductID AND PCheck.PaymentMethod = 'Check'
LEFT JOIN Payments AS PCredit ON P.ProductID = PCredit.ProductID AND PCredit.PaymentMethod = 'Credit'
WHERE P.SaleDate = '2012-02-10' GROUP BY ProductID;

SUM CASE using example:

    SELECT 
  DISTINCT(p.`ProductID`) AS ProductID,
  SUM(IF(p.`PaymentMethod`='Cash',Amount,0)) AS Cash_,
  SUM(IF(p.`PaymentMethod`='Check',Amount,0)) AS Check_,
  SUM(IF(p.`PaymentMethod`='Credit Card',Amount,0)) AS Credit_Card_,
  SUM( CASE PaymentMethod 
      WHEN 'Cash' THEN Amount
      WHEN 'Check' THEN Amount
      WHEN 'Credit Card' THEN Amount
     END) AS Total
FROM
  `payments` AS p 
GROUP BY p.`ProductID`;

SQL FIDDLE: http://www.sqlfiddle.com/#!9/23d07d/18

This might be seen as a little complex but does exactly what you want

SELECT 
  DISTINCT(p.`ProductID`) AS ProductID,
  SUM(pl.CashAmount) AS Cash,
  SUM(pr.CashAmount) AS `Check`,
  SUM(px.CashAmount) AS `Credit Card`,
  SUM(pl.CashAmount) + SUM(pr.CashAmount) +SUM(px.CashAmount) AS Amount
FROM
  `payments` AS p 
  LEFT JOIN (SELECT ProductID,PaymentMethod , IFNULL(Amount,0) AS CashAmount FROM payments WHERE PaymentMethod = 'Cash' GROUP BY ProductID , PaymentMethod ) AS pl 
    ON pl.`PaymentMethod` = p.`PaymentMethod` AND pl.ProductID = p.`ProductID`
  LEFT JOIN (SELECT ProductID,PaymentMethod , IFNULL(Amount,0) AS CashAmount FROM payments WHERE PaymentMethod = 'Check' GROUP BY ProductID , PaymentMethod) AS pr 
    ON pr.`PaymentMethod` = p.`PaymentMethod` AND pr.ProductID = p.`ProductID`
  LEFT JOIN (SELECT ProductID, PaymentMethod , IFNULL(Amount,0) AS CashAmount FROM payments WHERE PaymentMethod = 'Credit Card' GROUP BY ProductID , PaymentMethod) AS px 
    ON px.`PaymentMethod` = p.`PaymentMethod` AND px.ProductID = p.`ProductID`
GROUP BY p.`ProductID` ;

Output

ProductID | Cash | Check | Credit Card | Amount
-----------------------------------------------
    3     | 20   |  15   |   25        |  60
    4     | 5    |  6    |   7         |  18

SQL Fiddle Demo