Question

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 1

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

Step-by-step 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:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C $20,000.00

time: n years

rate 0.10

PV $75,000.0000

`20000 * (1-(1+0.1)^(-n) )/(0.1) = 75000\\`

`(1+0.1)^(-n)= 1-(75000*0.1)/(20000)`

Now, we solve for what we can:

`(1+0.1)^(-n)= 0.625`

And apply logarithmics properties to solve for n

-4.931305661

4.93