`r = 8%, t = 35` 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 values A = 1000000, r = 0.08, and t = 35, the formula becomes:

 `1000000=P(1+0.08/n)^(n*35)`

Since the r is compounded monthly, then n=12.

`1000000=P(1+0.08/12)^(12*35)`

Isolating the P, it yields

`1000000/(1+0.08/12)^(12*35) = P`

`61377.75=P`

Therefore, the principal amount that should be invested is $61,377.75 .