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+0.075/n)^(n*20)`
Since the r is compounded monthly, the value of n is 12.
`1000000=P(1+0.075/12)^(12*20)`
Simplifying the right side, it becomes
`1000000=P(1+0.00625)^240`
`1000000=P(1.00625)^240`
Isolating the P, it yields
`1000000/1.00625^240=(P(1.00625)^240)/1.00625^240`
`224174.18=P`
Therefore, the principal amount that should be invested is $224,174.18 .
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