Use FV formula to calculate that:
1% = 100% x [1 - 1/60]^N
Divide both sides by 100%
0.01 =[ 0.9833333]^N
Take the the log of both sides:
N =log(0.01) / log(0.9833333)
N =274 people will take away EXACTLY 99% of the illnes.
S0: 274 + 1 = 275 people to take away AT LEAST 99% of the illness.