Rate

Xiao Hao wants to deposit an amount of \(\$120,000\) into a bank that pays a simple interest. He has three options of deposit plans:

Option A : Simple interest rate of \(2.75\%\) per annum.

Option B : Simple interest rate of \(2.15\%\) for the first annum, with an increment of \(0.30\%\) for each of the following years, but no more than \(3.05\%\).

Option C : Simple interest rate of \(2.50\%\) for the part of deposit below \(\$90,000\); Simple interest rate of \(3.25\%\) for the part of deposit above \(\$90,000\).

1. If Xiao Hao decides to deposit the money for \(3\) years, find the total amount of interest he will receive for each option, respectively, and state which option is better in terms of the interest gained.
2. If Xiao Hao chooses Option A, and received a total interest of \(\$13,200\), find the number of years he deposits his money.
3. Find the least number of years Xiao Hao should deposit his money for Option B to yield a higher total amount of interest than Option A.
4. Find the least amount of money one should deposit for Option C to yield a higher amount of interest annually than Option A.