1 - Purdue University



(10 points)A 5 year monthly annuity immediate pays 100 per month. Calculate the accumulated value at the end of 5 years at an annual effective interest rate of 6%.

1. (10 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 |5 |100 |

|5 |5 |100 |

|6 |0 |50 |

Calculate the Net Present Value at 12%.

2. (15 points)A 10 year increasing annuity immediate pays 1000 at the end of year 1, 1000+X at the end of year 2 and 1000+2X at the end of year 3. Each subsequent payment pays X more than the previous payment until the last payment is made at the end of 10 years. You are given accumulated value of this annuity is 14,480.67 and (1+i)10 = 2. Calculate X.

3. (10 points)An annual perpetuity immediate pays 100X at the end of year X. In other words, 100 at the end of year 1, 200 at the end of year 2, 300 at the end of year 3, etc. The present value of the perpetuity is 42,000. Calculate i.

a. 4.00%

b. 5.00%

c. 6.00%

d. 7.00%

e. 8.00%

4. (20 points)Calculate the accumulated value at a constant force of interest of 5% of a 20 year continuous annuity which pays at the rate of (t+1)/2 per period at exact moment t.

5. (10 points)An annuity pays 1000 at the end of each year for 8 years. Calculate the present value of the annuity using a nominal quarterly interest rate of 8%.

6. (15 points)A monthly increasing annuity immediate pays 10 at the end of the first month, 20 at the end of the second month and 30 at the end of the third month. Payments continue to increase by 10 each month until 360 is paid at the end of the 36 month. Calculate the present value of this annuity at an annual effective interest rate of 12%.

7. (10 points)Andres invests 1000 at the beginning of each year for 10 years into a Fund A earning Y% each year. At the end of the year, any interest earned is moved to Fund B which earns 5%. Combining both Funds, Andres has a total of 11,924.08 at the end of 10 years. Determine Y.

a. 0.00%

b. 1.00%

c. 2.00%

d. 3.00%

e. 4.00%

8. (15 points)A 5-year increasing annuity immediate pays 10 at the end of each quarter during year 1, 20 at the end of each quarter during year 2, 30 at the end of each quarter during year 3, 40 at the end of each quarter during year 4, and 50 at the end of each quarter during year 5. Calculate the present value of this annuity at an annual effective interest rate of 6%.

9. (10 points)The following table lists the interest rate credited under an investment year method of crediting interest.

|Calendar Year of |First |Second Year |Third Year |Fourth Year |Fifth Year|Portfolio Rate |

|Investment |Year | | | | | |

|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 | | | | | |

Heather invests $1000 on January 1, 1998. Malik invests Z on January 1, 2003. On December 31, 2005, Malik and Heather have the same amount of money. Determine Z.

10. (15 points)A fund has 2000 at beginning of the year. Half way through the year, the fund value has increased to 2200 and an additional 1000 is invested. At the end of the year, the fund has a value of 3255. Which of the following are true:

i. The interest earned by the fund during the year is 255.

ii. The exact dollar weighted rate of return using compound interest is 10.25%.

iii. The estimated dollar weighted rate of return using the assumptions that 1-tit = (1-t)i is 10.2%.

iv. The time weighted rate of return is 11.9%.

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) The correct answer is not given by (a), (b), (c), or (d).

11. (10 points)A deferred annuity pays 100 at the end of year 10. Each annual payment thereafter is equal to 110% of the previous payment. (Therefore, 110 is paid at the end of year 11, 121 is paid at the end of year 12, etc.) The last payment is made at the end of year 20. Calculate the present value of this deferred annuity at an annual effective interest rate of 8%.

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