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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