Try this: Substitute your receipt column to 1 for "yes" and 0 for "no" (alternatively create a formula in the column E to the right as "=if("yes",1,0)).
Then in D1, use =subtotal(1,D3:D8).
(I tested in OpenOffice Calc, but Excel is basically the same and should work straight away)
| | | | =subtotal(1,D3:D8) |
|-------+--------+--------+--------------------|
| Name | Vendor | Amount | Receipt |
|-------+--------+--------+--------------------|
| John | A | 5 | 0 |
| John | B | 10 | 1 |
| John | C | 15 | 0 |
| Bill | D | 10 | 0 |
| Sarah | E | 25 | 1 |
| Sarah | F | 5 | 0 |
|-------+--------+--------+--------------------|
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