Solve the following mathematical problems:

A senior citizen invest Tk. 50 lac in a fixed deposit scheme at 11.5% annual interest for six months. In every six months he withdraws Tk. 2 lac from his principal plus interest earned. What will be his principal amount to invest after two years?

Differentiate financial and economic costs with suitable example. The total revenue (TR) and Average Cost (AC) functions of a firm are given by $$\begin{gathered} TR=4350Q-13Q^2 \\ AC=Q^2-5.5Q +150+675Q^2 \end{gathered}$$ Where Q refers to quantity of output. Find the profit maximizing level of output and maximum profit.

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output,

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What are the tax revenue at equilibrium output? Does the government have a balanced budget?

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output when investment increases from $70 to $90.

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What has happened to the relationship of government spending and tax revenues? Why?