We can calculate the number of payments period by using the following formula in excel:-

=nper(rate,pmt,-pv,fv)

Here,

Nper = Number of payments period (monthly)

Rate = 3.5%/12 = 0.2917% (monthly)

Pmt = 0

PV = $100

FV = $100*3 = $300

Substituting the values in formula:

= nper(0.2917%,0,-100,300)

= 377.22 months

Number of years = Nper / 12

= 377.22 / 12

= 31.43 years