# What is the present value of the perpetuity?

Question 1.  Sarah Wiggum would like to make a single investment and have \$1.6 million at the time of her retirement in 35 years. She has found a retirement fund that will earn 3% annually. How much will Sarah have to invest today? If she earned an annual return of 20%, how soon could she then retire?

Question 2.  Much to your surprise, you were selected to appear on the TV show, “The Price is Right.” As a result of your prowess in identifying how many rolls of toilet paper an average American family keeps on hand, you win the opportunity to choose one of the following: \$2,000 today, \$10,000 in 10 years, or \$31,000 in 29 years. Assuming you can earn 16% on your money, which should you choose?

Question 3.  What is the present value of a \$650 perpetuity discounted back to the present at 10%? What is the present value of the perpetuity?

Question 4.  Alex Karez has taken out a loan of \$180,000 with an annual rate of 10% compounded monthly to pay off hospital bills from his wife’s illness. If the most Alex can afford to pay is \$3,500 a month, how long will it take to pay off the loan? How long will it take to pay off the loan if he can pay \$4,000 each month? Use five decimal places for the monthly percentage rate in your calculations. If Alex can pay \$3,500 a month, how many years will it take to pay off the loan?

Question 5.
You are given three investment alternatives to analyze. The cash flows from these three investments are as follows:
What is the present value of investments A, B, and C if the appropriate discount rate is 10%?
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