Friday, November 16, 2012

`r = 7.5% , t = 20` 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+0.075/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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