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.

a. 4.44 years
b. 6.56 years
c. 5.97 years
d. 5.42 years
e. 4.93 years

Answer 1

To determine how long you can operate before requiring cash from the new business, we can use the formula for compound interest to calculate the future value of the $75,000 investment at a 10% annual rate of return. The calculation shows that you can receive payments of $20,000 per year for approximately Option a.4.44 years before requiring cash from the new business.

Step-by-step explanation:

To determine how long you can operate before requiring cash from the new business, we need to calculate the future value of the $75,000 investment at a 10% annual rate of return. We can use the formula for compound interest:

Future Value = Present Value × (1 + Interest Rate)^Time

Where:

• Present Value = $75,000 (the initial investment)
• Interest Rate = 10% per year
• Time = the number of years before you require cash from the new business

Now, let's calculate the time:

$75,000 × (1 + 0.10)^Time = $20,000

Solving for Time:

(1.10)^Time = 20,000/75,000

Time = log(20,000/75,000) / log(1.10)

Using a calculator, we find that Time is approximately 4.44 years.