John Bridgewater, 76, from Victoria, central London, targeted the girl after helping her parents look after her.
London's Southwark Crown Court heard he forced her to have sex just before her 16th birthday and shortly after it.
Bridgewater had repeatedly insisted the girl had consented to sex but the jury decided he was lying and convicted him on two counts of rape.
'Sexual remarks'
The jury were unable to reach verdicts on two further indecent assault allegations and one of rape.
Remanding him in custody for a pre-sentence report, Judge Gregory Stone warned Bridgewater to expect prison when he is sentenced next month.
Fiona Horlick, prosecuting, had told the court that as well as Bridgewater suggesting he film his victim having sex with other men, he also attempted to seduce a second young girl by showering her with cigarettes and money.
The court also heard he made sexual remarks to a third girl he plied with alcohol.
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