Your mother just won $250,249 from spitting a Nobal Prize with three coworkers.
ID: 2812035 • Letter: Y
Question
Your mother just won $250,249 from spitting a Nobal Prize with three coworkers. If she ivests her prize money in a diversified squity portfolio retuming 8 peroent per year, approimately how lng will it take her to become a millionaire, befre aocounting far taxes? Click on the table icon to view the FVIF table If she invests her príze money in a diversified equity porfolio relurning 3 percent per year, to become a milionaire before acccunting for taxes, il will take hyears Round to the nearest year)Explanation / Answer
Answer: 18 years
Given,
PV = Present value = prize money to be invested = $ 250,249
r = Interest rate = 8 % p.a. = 0.08 per annum per $
She wanted to be millionaire,
so,
FV = Future value = 1 million = $1000,000
We know that,
Compounding interest says,
FV = PV * ( 1+r )n
Where, FV = future value
PV = Present value
r = interest rate
n = no. of years
Therefore,
FV = PV * ( 1+r )n
==> ( 1+r )n = FV/PV
Apply log on both sides,
==> log (1+r)n = log (FV/PV)
==> n log (1+r) = log ( $1000000/$250,249)
==> n = log ( $1000000/$250,249) / log (1+r) = log ( $1000000/$250,249) / log (1+0.08)
==> n = 18 years
Therefore, no.of years required to become millionaire = n = 18 years
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