I would also like the the result to be precise to hour (or minute).
It is for a java program.
I have looked around, but the service I have found could not satisfy my need:
http://www.coindesk.com/api/: only precise to date
https://api.coinbase.com/v1/prices/historical?page=1 (from https://community.coinbase.com/t/past-bitcoin-exchange-rates/1725): need to adjust page number to find the desired time (at which one wants the value of exchange rate)
http://api.bitcoincharts.com/v1/csv/: I am not exactly sure what it does, but it seems that one needs to download different files from this site containing “USD” in the file names, check in all the files before finding the desired time