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Suppose you won a $75,000 after-tax cash prize in the lottery. You want to start a new business that you think will lose money for a while, after which it will be up and running and bringing in big bucks. You plan to invest the funds immediately in securities that are expected to earn 10% per year. Suppose you would need only $20,000 per year during the start-up period. How long could you operate before you would require cash from the new business, i.e., how long could you receive payments of $20,000 per year? The first withdrawal will be made a year from today, and your answer will contain a fraction of a year.

Answer :

TomShelby

Answer:

how long could you receive payments of $20,000 per year?

for almost 5 years. (4.93)

It could be made 4.93 withdrawals of 20,000

which means 4 of 20,000

and one for 9% of 20,000 = 18,600

Explanation:

we should consider how many years can the prize fund the new business start-up period of 20,000 dollars per year

considering it can yield 10% per year.

we need to sovle for time in an annuity:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C  $20,000.00

time: n years

rate 0.10

PV $75,000.0000

[tex]20000 \times \frac{1-(1+0.1)^{-n} }{0.1} = 75000\\[/tex]

[tex](1+0.1)^{-n}= 1-\frac{75000\times0.1}{20000}[/tex]

Now, we solve for what we can:

[tex](1+0.1)^{-n}= 0.625[/tex]

And apply logarithmics properties to solve for n

[tex]-n= \frac{log0.625}{log(1+0.1)[/tex]

-4.931305661

4.93

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