Question 987257: You have just won $150,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 6% compounded weekly, how long do you have to wait to become a millionaire?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! P=Po{1+r/n}^nt
P/Po=6.67 (a million over 150,000)
6.67=(1+.06/52)^52t
without rounding the 6.67, take ln of both sides
1.8971=52t ln (1.0011); ln 1.011, the not rounded, is 0.00115. Divide both sides by this.
31.64 years (rounded)
;
check is with rule of 72. The money will double in 72/6=12 years. It will take 24 years to quadruple, and 48 years to increase eightfold. The answer is in the range of sensibility.
put another way, (1.06)^31.64 should be near but below 6 2/3, since the interest is compounded weekly and not annually. 1.06^31.64 is 6.31.
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