Consider the irregular cash flow shown above and assume that the money is invested in an account that earns $10\%$ annual

interest. What is the value of $x$ at $t=5$ to ensure that the cash flow shown has a future value of $$2,000$ at $t=5?$ Calculate your

answer to the nearest dollar.

Alex invested in a new start$-$up project. Due to the start$-$up project's nature, Alex will not receive any returns for the

first $3$ years. Alex is expected to receive equal annual payments beginning at the end of $t=4$ for the next $5$ years from

the company as a return on his investment. The start$-$up company promised to pay $$3,000$ at the end of each year

during this period. They promised that they will let Alex know how much she should invest today to ensure these

cash flows. Assume that the project will offer a rate of return of $6\%.$ Use this information to answer the following

questions.

Question $12$

How much should Alex invest to generate the cash flows described above?