CFA Fundamentals - Chapter 1 Q&A Flashcards
A student has $25,000 in her bank account, and the University charges a total of $500 per credit hour. How many credit hours can she purchase before she must borrow money?
A. 5.
B. 12.
C. 50.
D 150.
C
let n represent the number of credit hours (the unknown). We know that the number of hours multiplied by the cost per hour, $500, yields the total spent, which cannot be more than $25,000. We represent this in equation form as the following:
$500n = $25,000
n = $25,000 / $500 = 50
If 15 / c = 3, which of the following represents the value of c?
A. 3.
B. 5.
C. 15.
D. 45.
B
Multiplying both sides of the equation by c, we are left with the following:
15 = 3C
C = (15/3)
C = 5
If p ≤ 25 / 5, which of the following represents the value of p?
A. L less than or equal to 5.
B. Greater than or equal to 5.
C. Equal to 5.
D. Equal to 25.
A
dividing 25 by 5, we are left with p ≤ 5. The ≤ sign indicates “less than or equal to,” so the interpretation of the equation is p is less than or equal to 5.
In the equation 3(x + 5) = 45, which of the following represents the value of x?
A. 10.
B. 15.
C. 20.
D. 25.
A
First we multiply through the parentheses by 3 and are left with 3x + 15 = 45. We then subtract 15 from both sides and get 3x = 30. Dividing both sides by 3 leaves us with x = 10.
If 4x + 4y = 24 and 2x + 3y = 24, which of the following statements is TRUE?
A. x = 6.
B. x = 12.
C. y = 6.
D. y = 12.
D
First set up the equations as simultaneous equations:
- Equation 1: 4x + 4y = 24
- Equation 2: 2x + 3y = 24
Sub one equation into another:
- 4x = 24 - 4y
- x = 6 - y
- Sub:
- 2(6 - y) + 3y = 24
- 12 - 2y + 3y = 24
- 12 + y = 24
- y = 12
- Sub:
- 4x + 4(12) = 24
- 4x + 48 = 24
- 4x = -24
- x = -6
If x = 2 – y and y = x – 4, which of the following relationships is TRUE?
A. x = 3.
B. x = 6.
C. y = 1.
D. y = 14.
A
First set up the simultaneous equations:
- x = 2 - y
- y = x - 4
Sub
- y = 2 - y - 4
- 2y = -2
- y = -1
Sub
- x = 2 - (-1)
- x = 3
Jill invested $100,000 in stocks and bonds. Equities earned a total return of 12%, and the fixed income component earned 8%. If she had invested twice as much in equities, she would have made $1,800 more. How much was invested in equities?
A. $45,000.
B. $10,000.
C. $90,000.
DX. $55,000.
A
Define the variable, set up an equation based on the information, and solve for the variable.
- x = amount of money invested in equities
- $100,000 - x = amount invested in bonds
0.12x + 0.08(100,000 - x) + 1,800 = 0.12(2x) + 0.08(100,000 - 2x)
Left Side
- Equity Rate of Return + Bond Rate of Return + Increased Amount
Right Side
- Double Equity Rate of Return + Bond Rate of Return on Half of Bond Amount
A client invested $1.5 million both in stocks earning 13% total return and in bonds earning 5%. Total earnings for the clients was $143,000. What percentage was invested in fixed income?
A. 17.2%.
B. 25.4%.
C. 43.3%.
D. 85.9%.
C
Set up two equations:
- x = equities
- 1,500,000 - x = bonds
- 0.13(x) + 0.05(1,500,000 - x) = $143,000
- .13x + 75,000 - .05x = $143,000
- .08x = 68,000
- 850,000 = equities
- 650,000 = bond
650,000 / 1,500,000 = 43.3%
For a given present value and interest rate, the future value:
A. increases as the number of compounding periods per year increases.
B. decreases as the number of compounding periods per year increases.
C. remains the same as the number of compounding periods per year increases.
D. remains the same as the number of compounding periods per year decreases.
A. increases as the number of compounding periods per year increases.
As illustrated in the equation
(1 + i/m)m
the effective interest rate increases as the number of compounding periods per year, m, increases. As the effective rate increases, the future value increases since you are compounding at a higher rate.
For a given future value and interest rate, the present value:
A. increases as the number of compounding periods per year increases.
B. decreases as the number of compounding periods per year increases.
C. remains the same as the number of compounding periods per year increases.
D. remains the same as the number of compounding periods per year decreases.
B. decreases as the number of compounding periods per year increases.
As the effective rate increases, the present value must decrease since you are discounting at a higher rate.
Jim Wilson is planning to purchase a high performance sports car for $100,000. He will finance the purchase with a 5-year fully amortized loan at an interest rate of 5.0% with payments due at the end of each year. What is the interest portion of the payment in year three and the remaining principal balance at the end of year three?
Interest Principal
A. $5,000 $42,948
B. $3,145 $30,708
C. $5,000 $30,708
D. $3,145 $42,948
When a loan is fully amortized, the payments are typically equal for the life of the loan, and each payment includes interest on the amount of the loan still outstanding (remaining principal) with the rest of the payment applied to the principal balance.
FIRST = The payment is found using the ordinary annuity method as follows:
–100,000 = PV
5 = I/Y
5 = N
CPT PMT = $23,097
Interest in each year equal the interest rate (5.0%) times the principal balance at the end of the previous year. For the third year, the interest portion of the payment is 0.05 × 62,900 = $3,145. The principal portion of the payment is 23,097 – 3,145 = $19,952. Thus the principal balance gets reduced to 62,900 – 19,952 = $42,948 at the end of year three. The following amortization table demonstrates the interest, principal, and outstanding balance for each of the five years the loan is outstanding.
Year 0 = $100,000 Balance
Year 1 = $81,903 Balance ($100,000 - $23,097)
- Interest pmt = $5,000 (100,000 x .05)
- Principal pmt = $18,097 (23,097 - 5,000)
Year 2 = $62,900 Balance ($81,903 - $23,097)
- Interest pmt = $4,095 (81,903 x .05)
- Principal pmt = $19,002 (23,097 - 4,095)
Year 3 = $42,948 Balance ($62,900- $23,097)
- Interest pmt = $3,145 (62,900 x .05)
- Principal pmt = $19,952 (23,097 - 3,145)
Year 4 = $21,998 Balance ($42,948 - $23,097)
- Interest pmt = $2,147 (42,948 x .05)
- Principal pmt = $20,950 (23,097 - 2,147)
Year 5 = $0 Balance ($21,998 - $23,097)
- Interest pmt = $1,100 (21,988 x .05)
- Principal pmt = $21,988 (23,097 - 1,100)
Samantha Tyson must decide which of four investments are the most attractive in terms of future value. The details of each investment opportunity are as follows:
1: $1,000 annuity due with an interest rate of 7.1% and annual payments for three years.
2: $2,800 invested at an interest rate of 7.0% compounded monthly for three years.
3: $1,000 ordinary annuity with an interest rate of 7.1% and annual payments for three years.
4: $2,800 invested at an interest rate of 7.0% compounded semiannually for three years.
D Begin by calculating the future value of each investment as follows:
- $1,000 annuity due with an interest rate of 7.1% and annual payments for three years.
- Begin
- Pmt = -1,000
- I/YR = 7.1
- N = 3
- FV = $3,447
- $2,800 invested at an interest rate of 7.0% compounded monthly for three years.
- No Payment
- PV = -2,800
- I/YR = 7.0
- N = 3*12 = 36
- FV = $3,452
- $1,000 ordinary annuity with an interest rate of 7.1% and annual payments for three years.
- End
- PMT = -1,000
- I/YR = 7.1
- N = 3
- FV = 3,218
- $2,800 invested at an interest rate of 7.0% compounded semiannually for three years.
- PV = -2,800
- I/YR = 7
- N = 6
- FV = $3,442
2,1,4,3
What is the value of $1,000 after 12 years at a semiannually compounded stated annual rate of 10%?
A. $2,200.
B. $3,138.
C. $3,225.
D. $3,600.
C
Future Value:
- PV = -1,000
- I/YR = 10%
- N = 24
- FV = $3,225
What is the value of $1,000 after 12 years at a quarterly compounded stated annual rate of 10%?
A. $3,271.
B. $3,304.
C. $2,200.
D. $3,385.
A
Future Value:
- PV = -1,000
- I/YR = 10%
- P/YR = 4
- N = 48
- FV = $3,271
What is the value today for a lump sum of $1,000 to be received 5 years from now, using a 10% rate of interest?
A. $500.
B. $621.
C. $667.
D. $909.
B
Future Value
- End or Beg
- FV = 1,000
- N = 5
- I/YR = 10%
- P/YR = 1
- PV = 621
