Get the price of a currency at specific time in the past using binance historical data api
Maybe the klines api will suit your needs: https://github.com/binance-exchange/binance-official-api-docs/blob/master/rest-api.md#klinecandlestick-data

Kline/Candlestick data

GET /api/v1/klines

Kline/candlestick bars for a symbol. Klines are uniquely identified by their open time.

Weight: 1

Parameters:
Name    Type    Mandatory   Description
symbol  STRING  YES     
interval    ENUM    YES     
startTime   LONG    NO  
endTime     LONG    NO  
limit   INT     NO  Default 500; max 1000.

    If startTime and endTime are not sent, the most recent klines are returned.

Response:

[
  [
    1499040000000,      // Open time
    "0.01634790",       // Open
    "0.80000000",       // High
    "0.01575800",       // Low
    "0.01577100",       // Close
    "148976.11427815",  // Volume
    1499644799999,      // Close time
    "2434.19055334",    // Quote asset volume
    308,                // Number of trades
    "1756.87402397",    // Taker buy base asset volume
    "28.46694368",      // Taker buy quote asset volume
    "17928899.62484339" // Ignore.
  ]
]