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Retirement Investment Planning Solutions with Calculations

Solve lump sum future value, interest rate, number of periods, present value problems. Calculate annuity future value, periods, payment for retirement planning with inflation consideration. Use equations, Excel, and calculators.

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Retirement Investment Planning Solutions with Calculations

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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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