Place a SUM to a cell based on the TYPE and MONTH in Excel 2010

We are trying to find a formula where it will read a series of values (date, type & amount) and accumulate thjem by the Type/Month.

Date		Type	Amount
01/01/16	BANK	$20.00 
01/15/16	BANK	$100.00 
02/05/16	CAR	$75.00 
03/06/16	BANK	$150.00 
03/20/16	CAR	$300.00 
04/02/16	CAR	$95.00 

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So based on the transactions above, we are trying find the correct formula that would calculate and display:

Type	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
BANK     $120.00       $150.00
CAR            $75.00   $300.00 $95.00

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The attached excel shows the formulas that have worked partially (SUMPRODUCT and SUMIF).

Please advice on a formula or combinations of formula that will give us the result expected.
SumByType-Month.xlsx