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Your money at Riverzxzxz Bank today is worth two million dollars. If you deposited this...

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spock9 | Student, Undergraduate | (Level 1) Honors

Posted May 16, 2012 at 6:42 AM via web

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Your money at Riverzxzxz Bank today is worth two million dollars. If you deposited this 5 years ago at 3% computed semiannually, what is the original principal?

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 16, 2012 at 9:30 AM (Answer #1)

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The formula for figuring compound interest is `A=P(1+r/t)^(nt)` where A is the amount at a given time, P is the principal (the amount initially invested), r is the rate, n is the number of times compounded per year, and t is the time in years.

Substituting the known values, we solve for P:

`2,000,000=P(1+(.03)/2)^(5*2)`

`2,000,000=P(1.015)^10`

`P=(2,000,000)/((1.015)^10)~~1,723,334.46`

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Thus the original deposit was $1,723,334.46

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** An alternative approach is to use the formula for present value:

`PV=(FV)/(1+r)^n` where PV is the present value, FV is the future value, r is the interest rate and n is the number of time periods.

Here the future value is 2,000,000, and we seek the present value.

`PV=(2,000,000)/(1+(.03)/2)^10~~1,723,334.46` as before.

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