1.What is the present value of a security that will pay $42,000 in 20 years if securities of equal risk pay 9% annually? Do not round intermediate calculations. Round your answer to the nearest cent.
2. Your parents will retire in 16 years. They currently have $370,000 saved, and they think they will need $2,150,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds? Round your answer to two decimal places.
3. You have $10,463.18 in a brokerage account, and you plan to deposit an additional $6,000 at the end of every future year until your account totals $250,000. You expect to earn 14% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number.
4. An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $400 at the end of Year 5, and $600 at the end of Year 6. If other investments of equal risk earn 6% annually, what is its present value? Its future value? Do not round intermediate calculations. Round your answers to the nearest cent.
Present value: $ ??
Future value: $ ??
5. Allison and Leslie, who are twins, just received $10,000 each for their 22th birthday. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her “early retirement fund” on her birthday, beginning a year from today. Allison opened an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 8% per year in the past. Leslie invested in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors have earned an average of 20% per year in the fund’s relatively short history.
a. If the two women’s funds earn the same returns in the future as in the past, how old will each be when she becomes a millionaire? Do not round intermediate calculations. Round your answers to two decimal places.
Allison: ??years
Leslie: ??years
b. How large would Allison’s annual contributions have to be for her to become a millionaire at the same age as Leslie, assuming their expected returns are realized? Do not round intermediate calculations. Round your answer to the nearest cent.
$??
c. Is it rational or irrational for Allison to invest in the bond fund rather than in stocks?
I. High expected returns in the market are almost always accompanied by a lot of risk. We couldn’t say whether Allison is rational or irrational, just that she seems to have less tolerance for risk than Leslie does.
II. High expected returns in the market are almost always accompanied by less risk. We couldn’t say whether Allison is rational or irrational, just that she seems to have more tolerance for risk than Leslie does.
III. High expected returns in the market are almost always accompanied by a lot of risk. We couldn’t say whether Allison is rational or irrational, just that she seems to have more tolerance for risk than Leslie does.
IV. High expected returns in the market are almost always accompanied by less risk. We couldn’t say whether Allison is rational or irrational, just that she seems to have less tolerance for risk than Leslie does.
V. High expected returns in the market are almost always accompanied by a lot of risk. We couldn’t say whether Allison is rational or irrational, just that she seems to have about the same tolerance for risk than Leslie does.
6.You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $8,000 at the end of the first year, and you anticipate that your annual savings will increase by 15% annually thereafter. Your expected annual return is 4%. How much will you have for a down payment at the end of Year 3? Do not round intermediate calculations. Round your answer to the nearest cent.
7. It is now December 31, 2020 (t = 0), and a jury just found in favor of a woman who sued the city for injuries sustained in a January 2019 accident. She requested recovery of lost wages plus $600,000 for pain and suffering plus $120,000 for legal expenses. Her doctor testified that she has been unable to work since the accident and that she will not be able to work in the future. She is now 62, and the jury decided that she would have worked for another 3 years. She was scheduled to have earned $38,000 in 2019. (To simplify this problem, assume that the entire annual salary amount would have been received on December 31, 2019.) Her employer testified that she probably would have received raises of 3% per year. The actual payment for the jury award will be made on December 31, 2021. The judge stipulated that all dollar amounts are to be adjusted to a present value basis on December 31, 2021, using a 7% annual interest rate and using compound, not simple, interest. Furthermore, he stipulated that the pain and suffering and legal expenses should be based on a December 31, 2020, date. How large a check must the city write on December 31, 2021? Do not round intermediate calculations. Round your answer to the nearest dollar.
8. Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $35,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 5%. He currently has $50,000 saved, and he expects to earn 7% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round intermediate calculations. Round your answer to the nearest dollar.
9.
A screenshot of a test Description automatically generated
A screenshot of a computer Description automatically generated
10.Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. Which of the following equations can be used to solve for the present value of an ordinary annuity?
· PMT x {1 – [1/(1 + r)nn]}/r
· PMT/r
· PMT x {[(1 + r)nn – 1]/r}
· PMT x {[(1 + r)nn – 1]/r} x (1 + r)
11. A screenshot of a graph Description automatically generated
Line A: ??
Line B: ??
Line C: ???
Investments and loans base their interest calculations on one of two possible methods: the ——– interest and the———– interest methods. Both methods apply three variables—the amount of principal, the interest rate, and the investment or deposit period—to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.
Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using:
Compound interest?
· FV = PV x (1 + I)NN
· FV = PV / (1 + I)NN
· FV = (1 + I)NN / PV
Simple interest?
· FV = PV – (PV x I x N)
· FV = PV + (PV x I x N)
· FV = PV / (PV x I x N)
Identify whether the following statements about the simple and compound interest methods are true or false.
Statement
True
False
Everything else held constant, an account that earns compound interest will grow more quickly than an otherwise identical account that earns simple interest.
After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.
All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year.
Heather is willing to invest $30,000 for six years, and is an economically rational investor. She has identified three investment alternatives (L, M, and P) that vary in their method of calculating interest and in the annual interest rate offered. Since she can only make one investment during the six-year investment period, complete the following table and indicate whether Heather should invest in each of the investments.
Note: When calculating each investment’s future value, assume that all interest is earned annually. The final value should be rounded to the nearest whole dollar.
Investment
Interest Rate and Method
Expected Future Value
Make this investment?
L
5% compound interest
M
4% simple interest
P
7% compound interest