Finance equations and formulas
1. What is the Rule of 72 ?
2. Solve using the Rule of 72: rate = 8%, years = 18, pv = $7,000. Solve for fv.
3. Solve, using the Rule of 72 rate = 4%, years = 18, fv=$8,000. Solve for pv.
4. Solve, using the Rule of 72: rate =6%, pv=$7,000, fv= $56,000. Solve for years.
5. Solve, using the Rule of 72: pv=$10,000; fv=$160,000; years=10. Solve for rate.
Q6-Q9. Use appropriate tvm table to solve Q6-Q9. For each question, cite the appropriate table that you are using, show the formula, and then plug-in your numbers to solve. Show all your work.
Q6 pv= $7,200 rate = 7% periods = 15 Solve for fv
Q7 fv=$15,000 rate = 15% periods = 10 Solve for pv
Q8 payment = $6,000 interest rate =8% number of periods = 10 Solve for pva
Q9 payment = $4,000 interest rate =10% number of periods = 20 Find fva
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 ?
The rule of 72 is a simple way of finding that in how many y