We are given the following information
Compound amount (future value) = P9000
Nominal interest rate = 9% = 0.09
Number of years = 4
Interest compounding = semi-annually means two times a year ( n = 2)
Recall that the present value is given by
[tex]PV=FV\cdot\frac{1}{(1+\frac{r}{n})^{n\cdot t}}[/tex]Where FV is the future value, r is the interest rate, n is the number of compoundings, and t is the number of years.
Let us substitute the given values into the above formula
[tex]\begin{gathered} PV=9000\cdot\frac{1}{(1+\frac{0.09}{2})^{2\cdot4}} \\ PV=9000\cdot\frac{1}{(1+0.045)^8} \\ PV=9000\cdot\frac{1}{(1.045)^8} \\ PV=9000\cdot0.703185 \\ PV=P6,328.7 \end{gathered}[/tex]So, the present value is P6,328.7
The amount of compounding interest is given by
[tex]\begin{gathered} CI=FV-PV \\ CI=9,000-6,328.7 \\ CI=P2,671.3 \end{gathered}[/tex]So, the compounding interest is P2,671.3
For part 3:
Interest compounding = Quarterly means 4 times a year (n = 4)
For part 4:
Interest compounding = Bi-monthly means 2 times a month so 2*12 = 24 times a year (n = 24)
For part 5:
Interest compounding = Annually means 1 time a year (n = 1)
