cfa study: quantitative methods [time value of money]

A client plans to send a child to college for four years starting 18 years from now. Having set aside money for tuition, she decides to plan for room and board also. She estimates these costs at $20,000 per year, payable at the beginning of each year, by the time her child goes to college. If she starts next year and makes 17 payments into a savings account paying 5 percent annually, what annual payments must she make?

2,744.50

The present value (PV) of an investment with the following year-end cash flows (CF) and a 12% required annual rate of return is closest to: YearCash Flow (€)1 100,000 2 150,000 5 -10,000

203,191

If the stated annual interest rate is 20% and the frequency of compounding is monthly, the effective annual rate (EAR) is closest to:

22%

A client invests €20,000 in a four-year certificate of deposit (CD) that annually pays interest of 3.5%. The annual CD interest payments are automatically reinvested in a separate savings account at a stated annual interest rate of 2% compounded monthly. At maturity, the value of the combined asset is closest to:

22,890

Given the following timeline and a discount rate of 4% a year compounded annually, the present value (PV), as of the end of Year 5 (PV5 ), of the $50,000 cash flow received at the end of Year 20 is closest to:

27,763

Suppose you plan to send your daughter to college in three years. You expect her to earn two-thirds of her tuition payment in scholarship money, so you estimate that your payments will be $10,000 a year for four years. To estimate whether you have set aside enough money, you ignore possible inflation in tuition payments and assume that you can earn 8 percent annually on your investments. How much should you set aside now to cover these payments?

28,396.15

A sports car, purchased for £200,000, is financed for five years at an annual rate of 6% compounded monthly. If the first payment is due in one month, the monthly payment is closest to:

3,867

A saver deposits the following amounts in an account paying a stated annual rate of 4%, compounded semiannually:YearEnd of Year Deposits ($) 1 4,000 2 8,000 3 7,000 4 10,000 At the end of Year 4, the value of the account is closest to:

30,447

Assume the following: The real risk-free rate of return is 3%. The expected inflation premium is 5%. The market-determined interest rate of a security is 12%. The sum of the default risk premium, liquidity premium, and maturity premium for the security is closest to:

4%

Using a discount rate of 5%, compounded monthly, the present value (PV) of $5,000 to be received three years from today is closest to:

4,305

An individual wants to be able to spend €80,000 per year for an anticipated 25 years in retirement. To fund this retirement account, he will make annual deposits of €6,608 at the end of each of his working years. He can earn 6% compounded annually on all investments. The minimum number of deposits that are needed to reach his retirement goal is closest to:

40

Given a stated annual interest rate of 6% compounded quarterly, the level amount that, deposited quarterly, will grow to £25,000 at the end of 10 years is closest to:

461

For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to: a. 555. b. 563. c. 576.

555

To cover the first year's total college tuition payments for his two children, a father will make a $75,000 payment five years from now. How much will he need to invest today to meet his first tuition goal if the investment earns 6 percent annually?

56,044.36

A consultant starts a project today that will last for three years. Her compensation package includes the following: Year End-of-Year Payment 1 $100,000 2 $150,000 3 $200,000 If she expects to invest these amounts at an annual interest rate of 3%, compounded annually until her retirement 10 years from now, the value at the end of 10 years is closest to:

566,466

A consumer purchases an automobile using a loan. The amount borrowed is €30,000, and the terms of the loan call for the loan to be repaid over five years using equal monthly payments with an annual nominal interest rate of 8% and monthly compounding. The monthly payment is closest to:

608.29

A financial contract offers to pay €1,200 per month for five years with the first payment made immediately. Assuming an annual discount rate of 6.5%, compounded monthly the present value of the contract is closest to

61,663

Grandparents are funding a newborn's future university tuition costs, estimated at $50,000/year for four years, with the first payment due as a lump sum in 18 years. Assuming a 6% effective annual rate, the required deposit today is closest to:

64,341

Two years from now, a client will receive the first of three annual payments of $20,000 from a small business project. If she can earn 9 percent annually on her investments and plans to retire in six years, how much will the three business project payments be worth at the time of her retirement?

77,894.21

A client can choose between receiving 10 annual $100,000 retirement payments, starting one year from today, or receiving a lump sum today. Knowing that he can invest at a rate of 5 percent annually, he has decided to take the lump sum. What lump sum today will be equivalent to the future annual payments?

772,173.49

A couple plans to set aside $20,000 per year in a conservative portfolio projected to earn 7 percent a year. If they make their first savings contribution one year from now, how much will they have at the end of 20 years?

819,909.8464

A client requires £100,000 one year from now. If the stated annual rate is 2.50% compounded weekly, the deposit needed today is closest to:

97,532

A bank quotes a stated annual interest rate of 4.00%. If that rate is equal to an effective annual rate of 4.08%, then the bank is compounding interest: a. daily. b. quarterly. c. semiannually.

a. daily

An investment pays €300 annually for five years, with the first payment occurring today. The present value (PV) of the investment discounted at a 4% annual rate is closest to: a. €1,336. b. €1,389. c. €1,625.

b. €1,389.

Given a €1,000,000 investment for four years with a stated annual rate of 3% compounded continuously, the difference in its interest earnings compared with the same investment compounded daily is closest to: a. €1. b. €6. c. €455.

b. €6.

The value in six years of $75,000 invested today at a stated annual interest rate of 7% compounded quarterly is closest to: a. $112,555. b. $113,330. c. $113,733.

c. $113,733

An investment of €500,000 today that grows to €800,000 after six years has a stated annual interest rate closest to: a. 7.5% compounded continuously. b. 7.7% compounded daily. c. 8.0% compounded semiannually.

c. 8.0% compounded semiannually

Which of the following risk premiums is most relevant in explaining the difference in yields between 30-year bonds issued by the US Treasury and 30-year bonds issued by a small private issuer? a. Inflation b. Maturity c. Liquidity

c. Liquidity

The nominal risk-free rate is best described as the sum of the real risk-free rate and a premium for: a. maturity. b. liquidity. c. expected inflation.

c. expected inflation.

A sweepstakes winner may select either a perpetuity of £2,000 a month beginning with the first payment in one month or an immediate lump sum payment of £350,000. If the annual discount rate is 6% compounded monthly, the present value of the perpetuity is: a. less than the lump sum. b. equal to the lump sum. c. greater than the lump sum.

c. greater than the lump sum

The stated (quoted) annual interest rate on an automobile loan is 10%. The effective annual rate (EAR) of the loan is 10.47%. The frequency of compounding per year for the loan is closest to

monthly

Once an investor chooses a particular course of action, the value forgone from alternative actions is best described as a(n):

opportunity cost

The minimum rate of return an investor must receive in order to accept an investment is best described as the:

required rate of return

The liquidity premium can best be described as compensation to investors for the

risk of loss relative to an investment's fair value if the investment needs to be converted to cash quickly

At a 5% interest rate per year compounded annually, the present value (PV) of a 10-year ordinary annuity with annual payments of $2,000 is $15,443.47. The PV of a 10-year annuity due with the same interest rate and payments is closest to:

16,216

A couple plans to pay their child's college tuition for 4 years starting 18 years from now. The current annual cost of college is C$7,000, and they expect this cost to rise at an annual rate of 5 percent. In their planning, they assume that they can earn 6 percent annually. How much must they put aside each year, starting next year, if they plan to make 17 equal payments?

2,221.58

An investor deposits £2,000 into an account that pays 6% per annum compounded continuously. The value of the account at the end of four years is closest to

2,542

A bank offers an effective annual rate (EAR) of 12%. Assuming quarterly compounding, the stated annual interest rate is closest to:

11.49%

A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock's present value is closest to:

126

market determined interest rate (r)

RFR + IP + DRP + LP + MP