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Additional Solved Problems

Additional Solved Problems. Lump Sum Future Value. The Problem. You've received a $40,000 legal settlement. Your great-uncle recommends investing it for retirement in 27-years by “rolling over” one-year certificates of deposit (CDs) Your local bank has 3% 1-year CDs

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Additional Solved Problems

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  1. Additional Solved Problems Lump Sum Future Value

  2. The Problem • You've received a $40,000 legal settlement. Your great-uncle recommends investing it for retirement in 27-years by “rolling over” one-year certificates of deposit (CDs) • Your local bank has 3% 1-year CDs • How much will your investment be worth? • Comment.

  3. Solution by Equation

  4. Calculator Solution

  5. Additional Solved Problems Lump Sum Interest Rate

  6. The Problem • If you have five years to increase your money from $3,287 to $4,583, at what interest rate should you invest?

  7. Algebraic Solution

  8. Additional Solved Problems Lump Sum Number of periods

  9. The Problem • How many years would it take for an investment of $9,284 to grow to $22,450 if the interest rate is 7% p.a. ? • p.a. = per annum = per year

  10. Data Extraction • PV = $9,284 • FV = $22,450 • i = 7% p.a. • n = ?

  11. Solution by Equation

  12. Additional Solved Problems Lump Sum Present Value

  13. The Problem • If investment rates are 1% per month, and you have an investment that will produce $6,000 one hundred months from now, how much is your investment worth today?

  14. Data Extraction • FV = $6000 • PV = ? • n = 100 months • i = 1%

  15. Solution by Equation

  16. Calculator Solution

  17. Additional Solved Problems Future Value of Annuity

  18. The Problem • How much will I have available in my retirement account if I deposit $2,000 per year into an IRA bank that pays on average 16% per year if I plan to retire in 40 years time? • If inflation is 3% per year, what is the real value of this amount? • Comment about this plan, given that I expect to live 20-years beyond retirement

  19. Categorization • Here we are talking about an a sequence of annual payments, so it is some kind of annuity • The problem is written loosely, and there is no indication of when the first cash flow occurs, right now at year-0, or at the end of this “year” in year-1. Assume at the end of the year at the beginning of year 1

  20. Categorization (Continued) • The evaluation point is not completely clear, but appears to be exactly 40-years from now • We are then looking at the future value of a regular annuity • We are searching for a future cash flow • The problem is to find the FV of a regular annuity

  21. Data Extraction • Step 1: • Pmt = $2,000 • i = 16% • n = 40 • FV = ? • Step 2: • PV of FV @ 3%

  22. Solution by Equation

  23. Calculator Solution

  24. Solution using Excel

  25. Solution using Excel

  26. Additional Solved Problems FV of an Annuity Solve for Periods

  27. The Problem • Assume house inflation and salary inflation are about equal over time. • How long will it take to save for the (real) $30,000 deposit for a home, given I can save a (real) $500 per month? A real return of 0.5% per month is available. (Inflation is irrelevant here)

  28. Categorization • This is an annuity evaluated at a future time • It is not clear whether it is regular or due, assume regular • We solve for the number of periods

  29. Data Extraction • Everything is is in terms of real spending power. • FV = 30000 • pmt = -500 • i = 0.5% (Watch this one, the interest factor is 1.005, not 1.05 nor 1.5. This is an easy error to make.) • n = ?

  30. Solution by Equation

  31. Calculator Solution

  32. Additional Solved Problems Future Value of an Annuity Find Payment

  33. The Problem • How much must you save each year in order to have saved $150,000 towards your retirement in 30 years? You believe that you can obtain a return of 9% on your investment over the whole period at an acceptable level of risk

  34. Categorization • Routine saving is an annuity, and we know what its future value is. We are not told of the starting date of the investment. Assume a regular annuity • We solve for annual payment

  35. Data Extraction • FV = 150,000 • i = 9% • n = 30 • pmt = ?

  36. Solution by Equation

  37. Calculator Solution

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