Question

A deposit of 4,000 at 6.5% for 270 days

Answer 1

Some institutions use 360 days a year (because then they charge more interest than 365 days).

Assuming the 360 days a year rule, the the daily rate is
6.5% for a year, or 270/360*6.5% for 270 days.
The future amount is then
4000*(1+0.065*270/360)
=$4195 (simple interest).