The total accumulated value, including the principal sum P plus compounded interest I, is given by the formula: $A=P(1+\frac{r}{n}{)}^{nt}$ Suppose a principal amount of $$1,500$ is deposited in a bank paying an annual interest rate of $4\mathrm{.}3\%,$ compounded quarterly.

Then the balance after $6$ years is found by using the formula above, with P $=1500,$ r $=0\mathrm{.}043,$ n $=4,$ and t $=6$:$A=1500(1+\frac{0\mathrm{.}043}{4}{)}^{46}$~~$1938\mathrm{.}84.$ So the amount A after $6$ years is approximately $$1,938\mathrm{.}84.$

Write a Python function named calculate$\_$interest$\_$income to return the final amount given the original principal, the annual interest rate, the compounding frequency, the overall length of time the interest is applied. Return your value as a formatted floating point number rounded to the nearest penny. In your main program, calculate the final amount for a principal amount of $$2000\mathrm{.}00$ deposited in a bank paying an annual interest rate of $3\mathrm{.}0\%,$ compounded monthly for keeping $10$ years.