`r = 9%, t = 25` Find the principal P that must be invested at a rate r, compounded monthly, so that $1,000,000 will be available for...

The formula in compounding interest is

`A = P(1 + r/n)^(n*t)`

where 

A is the accumulated amount

P is the principal

r is the annual rate

n is the number of compounding periods in a year, and

t is the number of years.

Plugging in the given values, the formula becomes:

`1000000 = P(1 + 0.09/n)^(n*25)`

Since the r is compounded monthly, the value of n is 12. 

`1000000=P (1 + 0.09/12)^(12*25)`

The right side of the equation simplifies to

`1000000=P(1.0075)^300`

Isolating the P, it becomes

`1000000/1.0075^300 = P(1.0075)^300`

`106287.83=P`

Therefore, the principal amount that should be invested is $106,287.83 .