Quiz 2: Time value of money (weeks 3 and 4 and is based on material from chapters 4 to 5)

An investment has a present value of $5976 and is expected to be worth $10682 in 8 years time. What is the annual compound interest rate? (IMPORTANT Please type your answer in decimals e.g. 10.1% should be shown as 0.101.)

0.075 Use the unknown interest rate formula in Chapter 4:

If a $11629 investment is returning a continuously compounded return of 8.9% how much will you expect to have at the end of 14 years? (Please round your answer to the nearest dollar but exclude the $ sign when typing your answer.)

40427

If the interest rate is 6.3 percent per year, find the future value of a five year simple annuity with a $3,000 yearly payment. Select one: a. $15,016. b. $17,937. c. $17,013. d. $ 9,482. e. None of the above.

c Use the FV of annuities formula in Chapter 5:

If a $6821 investment is returning a continuously compounded return of 12.8% how much will you expect to have at the end of 6 years? (Please round your answer to the nearest dollar but exclude the $ sign when typing your answer.)

7752 Use the continuous compounding formula in Chapter 4:

What is the present value of $93433 that is to be received in 15 years time if you require a 18.2 percent return? (IMPORTANT Please round your answer to the nearest dollar but exclude the $ sign when typing your answer.)

7607

If you invest $7,000 every year for two years starting one year from now, you will receive $_____ at the end of two year period. Assume that the bank pays you 8.3 percent interest compounded annually. Select one: a. 7,581.00 b. 15,791.22 c. 14,581.00 d. 14,000.00 e. 15,162.00

Use the FV of annuities formula in Chapter 5: The correct answer is: 14,581.00

How much should you pay for a $1,000 par value bond with 10% annual coupon payment, and four years to maturity if comparable market interest rates are 8%? Select one: a. $936.60. b. $988.62. c. $1,000. d. $1,066.24. e. $1,331.20.

d

Calculate the present value of a market security that promises to pay $1,000 p.a. forever, assuming an interest rate of 5.5% per annum. Select one: a. $181.82. b. $947.87. c. $1,055. d. $2,871.98. e. $18,181.82.

e

If a company borrows $125,000 from the money markets at a simple interest rate of 6.8% p.a., how much does the company repay at the end of 180 days? Select one: a. $129,121.91. b. $129,191.78. c. $133,500.00. d. $186,643.84. e. $190,835.62.

b

If you borrow $400 from your flat mate for 180 days at 5% p.a. simple interest, how much do you repay? Select one: a. $400.00. b. $409.86. c. $420.00. d. $500.00. e. $600.00.

b

The earnings of GDP Company have grown from $2.00 per share to $4.00 per share over a nine year time period. Determine the compound annual growth interest rate: Select one: a. 11.1 percent. b. 8 percent. c. 22.2 percent. d. 100 percent. e. 50 percent.

b

The annually compounded rate of interest that is equivalent to an annual interest rate compounded more than once per year is known as the ____________ rate of interest. Select one: a. effective b. nominal c. stated d. annual e. None of these.

a

What is the future value at the end of year 5 of the following cash flows placed in a term deposit paying 7% p.a.: year 1, $3,000; Year 2, $2,000; year 3 to 5, $1,000? Select one: a. $9,174.93. b. $9,597.37. c. $9,667.37. d. $11,220.41. e. $11,269.19.

b Use the FV of multiple cash flows formula in Chapter 5: The correct answer is: $9,597.37.

You are trying to determine what a client will need to save each year in order to have $800,000 on their retirement. Your client expects to retire in 11 years and savings will be deposited into an investment fund that earns 9.0% per annum. What is the annual end of year deposit required to meet their goal?

Use the annuity (FV) - regular payments formula in Chapter 5: The correct answer is: 45557.33

Which of the following statements about annuities is correct? Select one: a. An ordinary annuity is an equal payment paid at the beginning of each period. b. An ordinary annuity is an equal payment paid at the end of each period that increases by an equal amount. c. An annuity due is an equal payment paid at the beginning of each period. d. An annuity due is an equal payment paid at the end of each period. e. An annuity due is an equal payment paid at the end of each period that increases by an equal amount.

c

What is the current price of a coupon bond that has a face value of $1,000, a yield of 8 percent, pays an annual coupon payment of $100 and matures in two years? Select one: a. $973.98. b. $1,344.33. c. $1,035.67. d. $1,065.34. e. None of the above.

c Use the bond price formula in Chapter 5:

What is the price of a coupon bond that has an annual coupon rate of 8.5%, a par value of $1000, and a maturity of three years when current market yields are 10%? Select one: a. $211.38. b. $898.84. c. $962.70. d. $1,255.0. e. None of the above.

c Use the bond price formula in Chapter 5:

What is the realised interest rate if you invest $30 000 and get back $45,000 at the end of 3 years? Select one: a. 2.38%. b. 12.93%. c. 14.47%. d. 22.22%. e. 50%.

c Use the unknown interest rate formula in Chapter 4:

What is the present value of $47303 that is to be received in 9 years time if you require a 6.2 percent return? (IMPORTANT Please round your answer to the nearest dollar but exclude the $ sign when typing your answer.)

Use the PV of a single amount formula in Chapter 4: 27528

What is the implied interest rate if you borrow $50,000 and promise to pay back $90,000 at the end of 8 years? Select one: a. 6.05%. b. 7.62%. c. 22.5%. d. 109.20%. e. 110.2%.

b

The process of finding present values is frequently called: Select one: a. annualising. b. compounding. c. discounting. d. leasing. e. division.

c

Suppose you deposit $480 at the end of each month into a savings account for the next five years. If the bank pays interest at 6.6% p.a. compounded monthly over the period, how much will you have in your account at the end of five years? Select one: a. $8,386.98. b. $11,443.09. c. $24,265.55. d. $27,384.08. e. $34,011.14.

Use the FV of annuities formula in Chapter 5: e However, note that we are given monthly rather than annual payments and interest is paid on a monthly basis. Therefore we need to 'tell' the formula that we have monthly data. So just like we did in equation 4.8 (see Chapter 4: Compounding frequency) wherever r is in the formula above this will become r/m (interest rate per month) and n will become nxm (total number of monthly periods). The variable m is the number of compounding periods per year - so in this question it will be 12 for months.

If a $1026 investment is returning a continuously compounded return of 13.8% how much will you expect to have at the end of 17 years? (Please round your answer to the nearest dollar but exclude the $ sign when typing your answer.)

Use the continuous compounding formula in Chapter 4: The correct answer is: 10715

If you receive $25,400 back as principal and interest for the deposit of $20,000 that you had made three years before, your deposit carried a simple interest of _______ percent per annum. Select one: a. 10 b. 12 c. 9 d. 8 e. 7

Use the simple interest rate formula in Chapter 4: The correct answer is: 9

If you invest $1,000 every year for three years starting one year from now, you will receive $______ at the end of the three year period. Assume that you earn 7.5 percent interest compounded annually. Select one: a. 3,472.91 b. 3,230.63 c. 3,000.00 d. 3,225.00 e. 3,213.33

b Use the FV of annuities formula in Chapter 5:

Calculate the present value of the following cash flows assuming they occur at the end of the year and the average interest rate over the period is 8.0% p.a.: Year 1, $4,560; Year 2, $8,760; Year 3, $5,543. Select one: a. $6,187.48. b. $16,132.72. c. $17,423.34. d. $17,593.70. e. None of the above.

b Use the PV of multiple cash flows formula in Chapter 5:

Find the present value of an investment that promises to pay $5,000 per year beginning one year from now, and lasting forever, when the interest rate is 10 percent per annum. Select one: a. $100,000. b. $ 50,000. c. $ 10,000. d. $ 55,000. e. None of these.

b Use the constant perpetuity formula in Chapter 5:

If your investment of $5,000 earns a simple interest of $2,250 in five years, the interest rate is ______ percent per annum. Select one: a. 8 b. 9 c. 7 d. 10 e. 11

b Use the simple interest rate formula in Chapter 4:

If an investor originally bought a six zero-coupon bond for $695 and sold it for its maturity value of $1,000 six years later, what is the annual rate of return on the bond over this period? Assume annual compounding.

b Use the unknown interest rate formula in Chapter 4:

If an investor originally bought a three zero-coupon bond for $850 and sold it for its maturity value of $1,000 three years later, what is the annual rate of return on the bond over this period? Assume annual compounding. Select one: a. 5.0%. b. 5.57%. c. 5.88%. d. 15%. e. 17.6%.

b Use the unknown interest rate formula in Chapter 4:

What is the present value of $12,000 payable in 120 days if the simple interest rate is 7.1% p.a.? Select one: a. $11,204.48. b. $11,726.28. c. $11,732.42. d. $12,000.00. e. $12,280.11.

b The correct answer is: $11,726.28. Use the simple interest formula in Chapter 4:

What is the future value of a $10,000 university tuition fund if the nominal rate of interest is 12 percent compounded monthly for five years? Select one: a. $17,623.42. b. $18,166.97 c. $16,105.10. d. $16,122.26. e. $18,166.97

b Use the FV with m compounding periods formula in Chapter 4:

An infinite stream of equal cash flows occurring at regular intervals is known as a(n) _________ Select one: a. regular annuity. b. annuity due. c. perpetuity. d. premium. e. None of these.

c

If a term deposit offers an interest rate of 7.5% p.a. compounding continuously, how much will an initial investment of $11,000 be worth after two years? Select one: a. $11,856.73. b. $12,650.00. c. $12,780.18. d. $23,713.45. e. $49,298.58.

c

The more frequent the compounding the: Select one: a. greater the present value. b. greater the amount deposited. c. greater the effective interest rate. d. None of the above. e. All of the above.

c

When the amount earned on a term deposit is added to the principal at the end of a specified time period, the concept is called: Select one: a. principal interest. b. discount interest. c. compound interest. This option is correct assuming it the combined interest and original amount is reinvested d. simple interest. e. future value.

c

Your grandparents put $1,000 into a savings account for you when you were born 20 years ago. This account has been earning interest at a compound rate of 7 percent per annum. What is its value today? Select one: a. $1,967. b. $3,026. c. $3,870. d. $3,583. e. $3,934

c

An insurance company offers you an end of year annuity of $48,000 per year for the next 20 years. They claim that your return over the period will be 9 percent. How much would you be willing to pay today for this annuity? Select one: a. $628,496. b. $429,600. c. $438,170. d. $408,672. e. None of the above.

c Use the PV of annuities formula in Chapter 5:

How much must be invested today in order to generate a five year annuity with end of the year payments of $10,000 that begins at the end of two years from now if the discount rate is 10%? Select one: a. $28,742.03. b. $31,328.82. c. $34,461.70. d. $37,907.87. e. $50,918.27.

c Calculate the PV at the beginning of year 2 (i.e. the end of year 1) using the PV of annuities formula in Chapter 5 (shown below). Then calculate the PV at year 0 using the PV of a single amount formula in Chapter 4. Discount back for 1 year as the PV annuity formula determines the value today but assumes cash flows occur at the end of each year.

You plan to fund your retirement by depositing $4,000 at the end of each year into a savings account over the next twenty years. If you can earn 7.5% on your savings, how much will you have at the end of the twentieth year? Select one: a. $86,000.00. b. $131,096.55. c. $173,218.73. d. $226,552.06. e. None of the above.

c Use the FV of annuities formula in Chapter 5:

The present value of a 5 year ordinary annuity, with an 8 percent annual interest rate and a $1,000 yearly payment is? Select one: a. $925. b. $2,100. c. $3,992. d. $5,867. e. None of the above.

c Use the PV of annuities formula in Chapter 5:

If interest rates are 6.6% p.a. compounded annually, the present value of $4,000 to be paid in two and quarter year's time is: Select one: a. $3,409.31. b. $3,433.48. c. $3,464.23. d. $3,482.80. e. None of the above.

c Use the PV of a single amount formula in Chapter 4:

Suppose you deposit $2,500 at the end of the year into a savings account for the next six years. If the bank pays interest at 6.4% p.a. compounded annually over the period, how much will you have in your account at the end of six years? Select one: a. $3,627.35. b. $7,600.17. c. $15,960.00. d. $17,614.88. e. $56,677.38.

d

The present value of an annuity of $1,500 for three years with a 10 percent rate of interest is _________. Select one: a. $3,567.22 b. $3,856.22 c. $4,276.94 d. $3,730.28 e. None of the above.

d Use the PV of annuities formula in Chapter 5:

If you were offered different deposit rates from an insurance company, which method would you prefer? Select one: a. 7 percent interest compounded annually. b. 7 percent simple interest. c. 7 percent compounded daily. d. 7 percent compounded continuously. e. Any of these.

d See Compound interest and future value in Chapter 4.

How much does the $1,000 to be received upon a bond's maturity in four years add to the bond's price if the comparable interest rates are 6%? Select one: a. $209.91. b. $260.00. c. $760.00. d. $792.09. e. None of the above.

d Use the PV of a single amount formula in Chapter 4:

If a $75,000 investment becomes $90,750 at the end of two years, then the compound interest per year is ______ percent. Select one: a. 7 b. 8 c. 9 d. 10 e. 11

d Use the unknown interest rate formula in Chapter 4:

At the prevailing annual interest rate of 12.0%, the present value of a perpetuity that pays $3,000 twice a year is: Select one: a. $18,000. b. $25,000. c. $36,000. d. $40,000. e. $50,000.

e

You have $10,000 to invest. If you invest it at 6.2% p.a. with interest compounded semiannually for two years, what will be the value of your investment at the end of the two years? Select one: a. $10,620.00. b. $10,629.61. c. $11,240.00. d. $11,278.44. e. $11,298.86.

e

You buy a property and agree to pay $25,000 one year from now and another $25,000 two years from now. If your interest rate is 9 percent, the present value of this annuity is $________. Select one: a. 22,935.78 b. 29,000.00 c. 21,000.42 d. 43,377.78 e. 43,977.78

e Use the PV of annuities formula in Chapter 5: