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if you want to save $5,000 before buying your first new car, and you have $3,000 right now to invest at 3% interest compounded monthly, how long will you have to wait?

Guest Apr 22, 2017
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5000 =  3000(1 + .03)^(12 * t)     where t is the time in years

 

Divide both sides by 3000

 

5/3  =  (1 + .03/12)^(12 * t)      take the log of both sides

 

log (5/3)  log (1+ .03/12)^(12*t)    and we can write

 

log (5/3)  =  (12 * t) log (1+ .03/12)

 

log (5/3)   = 12 * log (1+ .03/12) * t      divide both sides by  12*log (1.03/12)

 

log (5/3)  / [ 12 * log (1+ .03/12) ] =  t   ≈  17 years

 

 

 

cool cool cool

CPhill  Apr 22, 2017

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