# You Are Thinking of Buying a House for $150,000

Time Value Practice Problems

Annuity Problems: Assume payments are at the end of the period unless otherwise stated (directly or indirectly).

- Today, you put $1,000 in a mutual fund. If you earn 10% annually, how much will you have in the fund in 10 years?

- You put $1,000 in a mutual fund annually (end-of-year). If you earn 10% annually, how much will you have in the fund in 10 years?

- Today, you put $10,000 in a mutual fund. Starting in 12 months and every year for 10 years, you add $3,000 per year. If you earn 10% annually, how much will you have in the fund in 10 years?

- Your uncle would like you to invest in a start-up company that is in the early stages of finding a cure for aging. The company’s goal is to make every aspect of the human body replaceable which will result in infinite life. He claims your portion of the investment would be worth $1,000,000 in five years.

a.If you would like a 45 annual return, how much would you be willing to invest today?

b.If you invest $300,000, what is your expected annual return?

c.Based on a and b, should you invest?

d.If you invested the $300,000 and the investment was worth $5,000 in five years, what would be your annual return?

- Your grandma is considering investing in a bond with a $100 annual interest payment (end-of-year) that matures in 10 years. In 10 years, your grandma would receive $1,000. Grandma would like a 5% annual return. What would be the maximum amount your grandma should pay for the bonds?

- You are considering buying a house for $150,000. You have a downpayment of $30,000. Assume a 15 year, 6% mortgage, monthly payments. How much will your mortgage payment equal?

- Assume you invested the $30,000 at a 9% annual return rather than buy the house. How much would the $30,000 be worth in 10 years?

- What is your annual (compound) rate of return if you invest $10,000 now and receive $26,000 at the end of ten years?

- You would like to buy a NEW Porsche 911 in five years. The Porsche with the features you want costs $90,000 today. You expect new models to increase at the rate of 6 percent annually. Realistically, you think you could afford one in five years (you want to pay cash). What will a new Porsche cost in five years?

- You would like to buy a cigarette boat in four years. The boat with the condition you want costs $80,000 today. You expect appreciation at the rate of 4 percent annually. You plan on paying cash. Ignore taxes.

a. How much do you expect to pay for a boat in four years?

- If you believe you can save $10,000 annually (starting in 12 months) and increase your savings by 5% per year, what annual return will you have to earn in order to reach your goal?

- If the inflation rate is 8 percent per year for 5 years, how much money do you need in 5 years to equal $1 today?

12. Today, you figure you need $40,000 a year to live if you were going to retire today. If you are 40 and want to retire when you are 60, how much will you need (the first year only) at age 60if the inflation rate is 3 percent per year?

13. You have $25,000 invested in Sun Microsystems. You expect Sun to appreciate at 10% a year. You want to buy a new Ford SUV, current price $30,000. You expect the price of vehicles to increase at the rate of 3 percent. Will you have enough money to buy a new Ford SUV in five years? Assume no taxes.

14.You have a three year old son. You would like to pay for his first year of college 15 years from now. If tuition is $15,000 now and you expect it to go up at the rate of four percent, how much will the tuition be in 15 years?

15. You know that you will receive $500,000 when your grandmother dies. If inflation is expected to be 4% annually and she dies in 15 years, what is the value of your inheritance in today’s dollars?

- Your financial consultant told you should have $4,000,000 worth of investments by the time you retire in 35 years. If you have nothing saved right now and expect a 7 percent return, how much do you need to save annually (end-of-year, equal payments) to reach your goal?