Question

TVM:
1. You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account that will earn 14 percent. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10 percent a year. (That is, you plan to deposit $5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your account after five years?

2. Foster Industries has a project that has the following cash flows:
Year Cash Flow
0 -$300.00
1 100.00
2 125.43
3 90.12
4 ?
What cash flow will the project have to generate in the fourth year in order for the project to have a 15 percent rate of return?

3. John Keene recently invested $2,566.70 in a project that is promising to return 12 percent per year. The cash flows are expected to be as follows:
End of Year Cash Flow
1 $325
2 400
3 550
4 ?
5 750
6 800
What is the cash flow at the end of the 4th year?

4. You recently purchased a 20-year investment that pays you $100 at t = 1, $500 at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of each of the remaining 17 years. You purchased the investment for $5,544.87. Alternative investments of equal risk have a required return of 9 percent. What is the annual cash flow received at the end of each of the final 17 years, that is, what is X?

5. Find the present value of an income stream that has a negative flow of $100 per year for 3 years, a positive flow of $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year-end.

Please include full solutions for the problems, not just final answer so I know how to model these for similar problems, thank you :)

Answer 1

(1) The deposits come in at the beginning of every year starting from now. This implies that the first deposit comes in at the beginning of Year 1 or end of Year 0. Further, the deposits grow at a rate of 10% per annum and are a total of 5 in number.

Brokerage Account Interest Rate = 14 %

Deposit Timeline:

Year 0 = $ 5000

Year 1 = 5000 x 1.1 = $ 5500

Year 2 = 5500 x 1.1 = $ 6050

Year 3 = 6050 x 1.1 = $ 6655

Year 4 = 6655 x 1.1 = $ 7320.55

All these deposits come in at the end of the time period mentioned against them.

Therefore, Deposit Value at the end of Year 5 = 5000 x (1.14)^(5) + 5500 x (1.14)%(5) + 6050 x (1.14)^(3) + 6655 x (1.14)^(2) + 7320.55 x (1.14) = $ 44873.95999 or $ 44873.96 approximately

NOTE: Please raise separate queries for the solutions to the remaing unrelated questions.