The Value of Money Flashcards
practice questions
The amount an investor will have in 15 years if $1,000 is invested today at an annual interest rate of 9% will be closest to:
N = 15 I/Y = 9 PV = - 1,000 PMT = 0 CPT > FV $3,642.48
Fifty years ago, an investor bought a share of stock for $10. The stock has paid no dividends during this period, yet it has returned 20%, compound annually, over the past 50 years. If this is true, the share price is now closest to:
N = 50 I/Y = 20 PV = - 10 PMT = 0 CPT > FV $91,004.38
How much must be invested today at 0% to have $100 in three years?
because no interest is earned, $100 is needed today to have $100 in three years.
How much must be invested today, at 8% interest, to accumulate enough to retire $10,000 debt due seven years from today? The amount that must be invested today is closest to:
N = 7 I/Y = 8 FV = - 10,000 PMT = 0 CPT > PV $5,834.90
The analyst estimates that XYZ’s earnings will grow $3.00 a share to $4.50 per share over the next eight years. The rate of growth in XYZ’s earnings is closest to:
N = 8 PV = -3 FV = 4.5 PMT = 0 CPT > I/Y 5.1989
If $5,000 is invested in a fund offering a rate of return of 12% per year, approximately how many years will it take for the investment to reach $10,000?
PV = -5,000 I/Y = 12 FV = - 10,000 PMT = 0 CPT > N 6.12
Rule of 72 > 72/12 = 6 years.
Note HP 12C users: A known problem which the HP 12C is that it will not accurately compute the number of periods in time value of money problems when the number of periods is not a round number. In this particular question, your HP 12C will give you an answer of 7, although the correct answer is 6.1163
An investment is expected to produce the cash flows of $500, $200, and $800 at the end of the next three years. If the required rate of return is 12%, the present value of this investment is:
Using your cash flow keys, CF(0) = 0 CF(1) = 500 CF(2) = 200 CF(3) = 800 I/Y = 12 NPV = $1,175.29
or you can add up the present values of each single cash flow:
PV(1) = N = 1
FV = -500
I/Y = 12
CPT > PV = 446.43
PV(2) = N = 2
FV = -200
I/Y = 12
CPT > PV 159.44
PV (3) = N = 3
FV = -800
I/Y = 12
CPT > PV = 569.42
446.43 + 159.44 + 569.4 = $1,175.29
Given an 8.5% discount rate, an asset that generates cash flows of $10 in year 1, $20 in year 2, $10 in year 3, and is then sold for $150 at the end of year 4, has a present value of:
Using your cash flow keys
CF(0) = 0 CF(1) = 10 CF(2) = -20 CF(3) = 10 CF(4) = 150
I/Y = 8.5 NPV = $108.29
An investor has just won the lottery and will receive $50,000 per year at the end of each of the next 20 years. At a 10% interest rate, the present value of the winnings is:
N = 20 I/Y = 10 PMT = -50,000 FV = 0
CPT > PMT = $425,678.19
If $10,000 is invested today in an account that earns interest at a rate of 9.5%, what is the value of the equal withdrawals that can be taken out of the account at the end of each of the next five years if the investor plans to deplete the account at the ned of the time period?
PV = -10,000 I/Y = 9.5 N = 5 FV = 0
CPT > PMT = $2,604.36
An investor is to receive a 15 year $8,000 annuity, the first payment to be received toady. At an 11% discount rate, this annuity’s worth today is;
This is an annuity due. Switch to BGN mode.
N = 15 PMT = -8,000 I/Y = 11 FV = 0
CPT > PV 63,854.92
(switch back to end mode)
Given an 11% rate of return, the amount that must be put into an investment account at the end of each of the next ten years in order to accumulate $60,000 to pay for a child’s education is closest to:
N = 10 I/Y = 11 FV = -60,000 PV = 0
CPT > PMT $3,588.08
An investor will receive an annuity of $4,000 a year for ten years. The first payment is to be received five years from today. At a 9% discount rate, this annuity’s worth today is:
Two steps: 1. Find the PV of the 10 year annuity N = 10 I/Y = 9 PMT = -4000 FV = 0 CPT > PV = 25,670.63
This is the PV as of the end of year 4.
2. Discount PV of the annuity back four years N = 4 PMT = 0 FV = -25,670.63 I/Y = 9 CPT > PV = 18,185.75
If $1,000 is invested today and $1,000 is invested at the beginning of each of the next three years at 12% interest (compounded annually), the amount an investor will have at the ned of the fourth year will be:
The key to this problem is to recognise that it is a 4-year annuity due, so switch to BGN mode:
N = 4 PMT = -1,000 PV = 0 I/Y = 12
CPT > FV = 5,352.84
(switch back to END mode)
An investor is looking at a $150,000 home. If 20% must be put down and the balance is financed at 9% over the next 30 years, what is the monthly mortgage payment?
N = 30 x 12 = 360 I/Y = 9/12 = 0.75 PV = -150,000(1-0.2) = -120,000 FV = 0
CPT > PMT = $965.55
