For Q10-Q13, you may use tvm tables, a financial calculator, or excel to solve.

Question

For Q10-Q13, you may use tvm tables, a financial calculator, or excel to solve. Be sure to show all the steps in your work: factors & formula if you use the tables; keystrokes if you use a financial calculator; or formulas if you use excel.

Q10. Stressed and penniless after months of day trading, Mr. Baruch decides to invest his savings into a conservative growth mutual fund. He plans to retire in 30 years and wants to make annual deposits into his IRA in order to accumulate a sum of $450,000 at the end of the 30 years. Mr. Baruch expects to earn 10% per year, on average, in his mutual fund. What should be the amount of Baruch's annual contributions ?

Q11. On the way to Stop&Shop, you buy a lottery ticket and win $100,000. The catch is that the money will be paid to to you in two installments: $50,000 today, and $50,000 at the end of 5 years from now.

Q11-a: Assuming an interest rate of 8%, what is the present value of your total lottery payments ?

Q11-b: Suppose that you invest the $50,000 winnings that you receive today and earn 8% annually for the next 5 years. What is the future value of your total lottery payments ?

12. Investor G. Loeb owns a 5-year, $1000 bond with a 5% coupon. If the yield to maturity on similar bonds is currently 10%, what is Mr. Loeb's bond worth today ?

13. A security analyst is forecasting dividends for Boston Electric over the next four years, as follows: $1 (Y1), $1.50 (Y2); $2.00 (Y3); $2.75 (Y4). In addition, the analyst expects that the stock could be sold for $62.25 four years from now. If the required return on the stock is  8%, what is the stock worth today?

Explanation / Answer

10) Now let annual payment = A

FV = A/r * [(1+r)^n - 1]

450000 = A/0.1*[(1.1)^30-1]

A = 2735.66

11) a) PV = FV/(1+r)^n

where r is rate of interest and n is number of perion

PV = 50000 + 50000/(1.08)^5 = 84029.16

b) FV = PV*(1+r)^n

where r is rate of interest and n is number of perion

so FV = 50000*(1.08)^5 + 50000 = 123466.40

12) 5% of 1000 = 50. So he will get $50 annualiy and 1000 at the end of 5 years.

here PV = A/r [1-1/(1+r)^n] + FV/(1+r)^n

PV = 50/0.1 [1-1/(1.1)^5] + 1000/(1.1)^5 = 810.46

13) PV = FV/(1+r)^n

where r is rate of interest and n is number of perion

PV = 1/(1.08) + 1.5/(1.08)^2 + 2/(1.08)^3 + 2.75/(1.08)^4 + 62.25/(1.08)^4 = 51.57

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