1 - mel3e and mel4e



Annuity Challenges – Finding Payment

1. Calculate the regular payment for each annuity. Each payment is made at the end of the compounding period.

a. Present value of $7835 at 6.77%. compounded annually for 15 years.

b. Present value of $8900 at 4.75% compounded semi-annually for 8.5 years.

c. Present value of $7500 at 7%. compounded quarterly for 6.5 years.

d. Present value of $2000 at 7.25%. compounded monthly for 1.5 years.

e. Present value of $15 500 at 4.85%. compounded semi-annually for 11.5 years.

f. Present value of $20 000 at 5.1%. compounded monthly for 9.25 years.

2. You deposit $3500 in an account that pays 5.8% compounded monthly. What equal withdrawals can you make each month for the next 3 years?

3. Megan’s trust fund has a present value of $15 000. She purchases an annuity that pays 6.4%. compounded semi-annually. How much can Megan withdraw every 6 months for the next 8 years?

4. Jeremy is a tri-athlete. His parents deposited $15 000 in an account that pays 7.25%. compounded monthly to help Jeremy with his training expenses. What equal monthly payment can Jeremy withdraw at the end of each month for the next 1.5 years?

5. Suppose you have $20 000 to purchase an annuity for the next 5 years. The interest rate is 8%. but the compounding period is flexible. You can chose monthly, quarterly, semi-annual or annual payments and compounding.

a) Determine the regular payment for each compounding period.

b) Determine the total amount received for each compounding period.

c) Which investment would you chose? Justify your choice.

|Solutions: | |

| | |

| |$106.16 |

|$847.79 |$1212.50 |

|$642.42 |$881.98 |

|$361.52 |a) Annual $5009.13; Semi-annually $2465.82; Quarterly $1223.13; monthly $405.53 |

|$117.60 |Annual $25045.65; Semi-annually $24658.20; Quarterly $24462.60; monthly $24331.80 |

|$887.16 |Annual payments because they have the greatest sum. |

|$226.39 | |

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