1. (10 points) A 20 year annuity has annual payments of 1700 at the end of each year. Calculate the accumulated value of the annuity at a nominal rate of interest of 6% compounded quarterly.
  1. (15 points) A fund has 4000 at beginning of the year. Half way through the year, the fund value has increased to 4200. At this point, 1000 is taken out of the fund. At the end of the year, the fund has a value of 3286.40. Which of the following are true:
  2. The interest earned by the fund during the year is 286.40.
  3. The exact dollar weighted rate of return using compound interest is 8.16%.
  4. The estimated dollar weighted rate of return using the assumptions that 1-tit = (1-t)i is 8.18%.
  5. The time weighted rate of return is 7.97%.

(a)All Items are true except for Item i.

(b)All Items are true except for Item ii.

(c)All Items are true except for Item iii.

(d)All Items are true except for Item iv.

(e)All Items are true.

  1. (10 points) Kevin is the beneficiary of an annuity with monthly payments of 100 for 15 years. Immediately before the first payment, Andrew offers to buy the annuity from Kevin. Assuming an annual effective interest rate of 8%, what is the amount that Andrew is offering to pay Kevin?
  1. (15 points) Joe is receiving a monthly annuity for 6 years. The annuity pays Joe P times the number of the payment at the end of each month. In other words, Joe receives P at the end of the first month, 2P at the end of the second month, 3P at the end of the third month, …, and 72P at the end of the last month. Joe invests the payments in a fund earning 7%. If Joe has 100,000 immediately after the last payment, calculate P.

  1. (10 points) The present value of a continuous perpetuity payable at a rate of 1000 per year is 20,000. Calculate i.
  1. 0.0476
  2. 0.0488
  3. 0.0500
  4. 0.0513
  5. 0.2500
  1. (15 points) Investment Project A has the following cash flows:

Year / Contributions / Returns
0 / 100 / 0
1 / 100 / 0
2 / 5 / 60
3 / 5 / 80
4 / 105 / 100
5 / 5 / 100
6 / 0 / 50

Which of the following are true:

  1. The net present value at 8% is 6.59.
  2. The net present value at the internal rate of return (yield) is 0.
  3. In determining the yield for this investment, it is possible to get up to three yield rates.
  1. All Items are true except for Item i.
  2. All Items are true except for Item ii
  3. All Items are true except for Item iii
  4. All Items are true.
  5. The correct answer is not given by (a), (b), (c), or (d).

  1. (15 points) An annuity immediate pays 20 at the end of each quarter during the first year, 40 at the end of each quarter during the second year, 60 at the end of each quarter during the third year, etc. The annuity pays 240 at the end of each quarter during the 12th year. There are no payments after the 12th year. Calculate the present value of this annuity if i = 6%.
  1. (15 points) A 10 year continuously increasing annuity pays at a rate of (1.05)t at time t. Calculate the present value of this annuity at i=10.25%.

  1. (15 points) A 10-year annual decreasing annuity pays 100,000 at the end of the first year. At the end of the second year, a payment of 95,000 is made. Each subsequent payment is 5000 less than the prior payment with 55,000 being paid at the end of the 10th year. Calculate the accumulated value of this annuity at an annual effective rate of 5%.
  1. (10 points) An 8-year annuity pays 2000 at the beginning of the first year. It pays 2400 at the beginning of the second year. It pays 2880 at the beginning of the third year with each subsequent payment equal to 120% of the previous payment. Calculate the present value of this annuity at 8% interest.

  1. (10 points) Jon invests 1000 at the start of each year for 10 years into Fund A earning 8% interest. At the end of each year, the interest earned is withdrawn and invested in Fund B earning 6%. How much will Jon have in both Funds combined at the end of 10 years?
  1. (10 points) The following table lists the interest rate credited under an investment year method of crediting interest.

Calendar Year of Investment / First Year / Second Year / Third Year / Fourth Year / Fifth Year / Portfolio Rate
1998 / .075 / .072 / .070 / .067 / .064 / .060
1999 / .070 / .068 / .065 / .062 / .060 / .055
2000 / .065 / .060 / .061 / .057 / .055 / .053
2001 / .055 / .052 / .048 / .046 / .045
2002 / .040 / .037 / .035 / .040
2003 / .030 / .032 / .037
2004 / .044 / .046
2005 / .050

Jenniferinvests $1000 on January 1, 1999. Jennifer also invests Z on January 1, 2004. On December 31, 2005, Jennifer has 2000. Determine Z.