1.   When i = .40, rank from smallest to largest:  1    , i ,  d ,  1  

A.   d,   i,   1   ,  1  

B.     1   ,  1   ,  i,  d

C.     1   ,  1   ,  d,  i

D.  d,   1    ,   1   ,  i

E.   None of the above

2.   If the accumulated value at time n of $1/yr paid continuously each year for n years is 10%    more than the accumulated value at time n of $1/yr paid at the end of each year for n years under the same interest rate assumption, then how does the present value at time zero of  an annuity of $1/yr paid at the end of each year for n years compare to the present value of an annuity of $1/yr paid continuously each year for n years?

A.     The annuity immediate is about  8% less

B.     The annuity immediate is about  9% less

C.     The annuity immediate is about 10% less

D.    The annuity immediate is about 10% greater

E.      Cannot be determined from the information given.

3.   When the annual effective interest rate is 30% and the number of years n is 3, which of the following most closely approximates the ratio of ̅   to      ?

A.   1.9

B.   2.0

C.   2.1

D.   2.2

E.   2.3

4.   Ann won 1st prize in the perpetuity lottery and gets $1,000 every other year forever with      her first payment due at the end of year 1. Ann’s friend Beth won second prize and receives $1,000 every other year forever but Beth’s first payment starts at the end of year 2. What is the present value at time zero of their combined winnings if d = .25 ?

A.   $1,000

B.   $2,000

C.   $3,000

D.  $4,000

E.   Over $4,000

5.   What is ( ∞    ∙  ∞    ∙  ∞    ) / (i ∙ d ∙ δ) when i= 10%?

A.   Close to zero

B.   1.00

C.   About 100,000

D.  About 500,000

E.   Over 1,000,000

6.    Jim’s annuity of $50/year is deferred for 10 years, then payable for 10 years with payments made at the start of each year.  If 50 ∙   10    = S, what is the present value of Jim’s annuity at time zero?

A.   $  ∙   17

B.   $  ∙   18

C.   $  ∙   19

D.  $ S ∙   20

E.   $  ∙   21

7.   When i = 25 %, what is  ∞     / ∞     ?

A.   1/2

B.   2/3

C.   3/4

D.  4/5

E.   None of the above

8.   Which of the following is not equivalent to the discount factor d?

A.    i/(1+i)

B.    iv

C.    1-v

D.   i/(  )

E.   None of the above

9.   Jack borrows $ 1,000 from his local bank which charges an annual effective interest rate of i for all their loans.  Later that same day, Jack decides to prepay the first year’s interest and   the bank agrees.  How much does Jack pay the bank that day?

A.    $ 1000 times  i

B.    $ 1000 times d

C.    $ 1000 times v

D.    $  i

E.    None of the above

10. Which of the following is closest to the portion of the present value of a continuous perpetuity that is paid in the first year when i = 50%?

A.     25 %

B.     27 %

C.     29 %

D.     31 %

E.     33 %

11.  What is the present value of an annuity immediate that pays $800 times the interest rate    each year for 3n years when interest is such that an investment of $1 doubles in value every n years?

A.    $  600

B.    $  650

C.    $  700

D.    $ 750

E.   None of the above

12. If the Accumulated Value at time t of an investment at time zero of $X is $X ∙ (.4+.4t), what is  when t=3?

A.    .20

B.    .25

C.    .30

D.    .35

E.    .40

13. Aaron and Bill share equally in the present value of an annuity due which has three annual   payments of $10 each.  If Aaron gets the entire 2nd payment and Bill gets the entire 3rd        payment, what portion of the 1st payment should Aaron receive?  Assume that the effective annual discount rate is 20%.

A.    36% of the first payment

B.    38% of the first payment

C.    40% of the first payment

D.   42% of the first payment

E.    46% of the first payment

14. What is the product of ( i, d3, v2, and (∞   )2  ) when d equals .1?

A.   .009

B.   .012

C.   .015

D.   .018

E.   None of the above.

15.   Which of the following statements is true?

I.              +   -    = 1

II.             =    when d=0

III.            =   3    +   ∙ −3    for n > 3

A.   I and II only

B.   I and III only

C.   II & III only

D.   II only

E.   I, II, and III

16.   If d = 6%, which of the following is true?

A.   5% < i < δ

B.   5% < δ < i

C.   i < δ < 5%

D.  δ < i < 5%

E.   Cannot be determined from the information given

17.  When i=d, and n=3, which of the following must equal −1   ∙     /     ?

A.   0

B.   1

C.   2

D.  3

E.   None of the above

18. Statement I : If the simple interest rate and the compound interest rate are equivalent, then the accumulated value at any time t of an initial deposit of $X using the compound interest rate is always greater.

Statement II : If i is unknown, then the value of d plus v cannot be determined. Statement III:  1    is greater than i for all values 0 < i < 1.

A.    Only statement I is true

B.    Only statement II is true

C.    Only statement III is true

D.   All 3 statements are false

E.    None of the above answers are correct

19.  Determine the simple interest rate i, such that the present value at time zero of a payment of $X at time 2 ½ years equals $0.8 ∙ X.

A.  8%

B.  9%

C.  10%

D.  12%

E.  None of the above

20. CALCULATOR PROBLEM: Alice makes deposits of $100 at time zero and $X at time 3.       Deposits grow at a constant force of interest δ=.04. The amount of interest earned from

time 3 to time 7 is $X.

Calculate X to the nearest dollar.

A.   $24

B.   $27

C.   $30

D.  $33

E.   $36