Fall 2011

Assignment 1

Solution

1. I need your group names! Groups of 4 people please.

2. You can deposit $10,000 into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today? Solution

Deposit now:Deposit in 10 years:

FV40=PV (1+k)40FV30=PV10 x (1+k)30

FV40=$10,000 x (1.09)40FV30=PV10 x (1.09)30

FV40=$314,090.00 (approx)FV30=$132,680.00 (approx)

You would be better off by $181,410 ($314,090 - $132,680) by investing the $10,000 now instead of waiting for 10 years to make the investment.

3. Assume that you just won the state lottery. Your prize can be taken either in the form of $40,000 at the end of each year for the next 25 years (i.e. $1,000,000 over 25 years) or as a single amount of $500,000 paid immediately. a. If you expect to be able to earn 5% annually on your investments over the next 25 years, ignoring taxes and other considerations, which alternative should you take? Why? b. Would your decision in part (a) change if you could earn 7% rather than 5% on your investments over the next 25 years? Why? Solution

a.

PVAn = PMT/k * (1-1/(1+k)^n)

PVA25 = $563,760

At 5%, taking the award as an annuity is better; the present value is $563,760, compared to receiving $500,000 as a lump sum.

b.

PVA25 = $466,160

At 7%, taking the award as a lump sum is better; the present value of the annuity is only $466,160, compared to the $500,000 lump sum payment.

4. For each of the mixed streams of cash flows shown in the following table, determine the future value at the end of the final year if deposits are made into an account paying annual interest of 12% assuming no withdrawals are made during the period and that the deposits are made: a. At the end of each year.

b. At the beginning of each year.

| |Cash Flow Stream |

|Year |A |B |C |

|1 |$900 |30,000 |1,200 |

|2 |1,000 |25,000 |1,200 |

|3 |1,200 |20,000 |1,000 |

|4 | |10,000 |1,900 |

|5 | |5,000 | |

a.

| |Cash Flow Stream | |Year |A | FV |B | FV |C |FV | |1 | $ 900.0 | $ 1,129.0 | $ 30,000.0 | $ 47,205.6 | $ 1,200.0 | $ 1,685.9 | |2 | $ 1,000.0 | $ 1,120.0 | $ 25,000.0 | $ 35,123.2 | $ 1,200.0 | $ 1,505.3 | |3 | $ 1,200.0 | $ 1,200.0 | $ 20,000.0 | $ 25,088.0 | $ 1,000.0 | $ 1,120.0 | |4 | | | $ 10,000.0 | $ 11,200.0 | $ 1,900.0 | $ 1,900.0 | |5 | | | $ 5,000.0 | $ 5,000.0 | | | |FV Sum | | $ 3,449.0 | | $ 123,616.8 | | $ 6,211.2 |

b. If payments are made at the beginning of each period the present value of each of the end-of-period cash flow streams will be multiplied by (1 + i) to get the present value of the beginning-of-period cash flows.

A$3,449.0 (1 + .12) = $3,862.50

B$123,616.8 (1 + .12) = $138,450.00

C$6,211.2 (1 + .12) = $$6,956.80

5. Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years and the credit union pays an annual interest rate of 8%. a. Determine the future value that Janet will have at the end of 10 years given that end of year deposits are made and no interest is withdrawn if: 1) $300...