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L5: Interest Formulas – Equal Payment Series

L5: Interest Formulas – Equal Payment Series. ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences. Equal Payment Series. F. 1. 2. N. 0. A. A. A. P. N. 0. 1. 2. N. 0. Equal Payment Series – Compound Amount Factor. F. 1. 2. N. 0.

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L5: Interest Formulas – Equal Payment Series

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  1. L5: Interest Formulas – Equal Payment Series ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

  2. Equal Payment Series F 1 2 N 0 A A A P N 0 1 2 N 0

  3. Equal Payment Series – Compound Amount Factor F 1 2 N 0 A A A F N 0 1 2 0 1 2 N A A A

  4. Compound Amount Factor F A(1+i)N-2 A A A A(1+i)N-1 N 1 2 N 0 1 2 0

  5. Equal Payment Series Compound Amount Factor (Future Value of an annuity) F 0 1 2 3 N A Example 2.9: • Given: A = $5,000, N = 5 years, and i = 6% • Find: F • Solution: F = $5,000(F/A,6%,5) = $28,185.46

  6. Validation

  7. Finding an Annuity Value F 0 1 2 3 N A = ? Example: • Given: F = $5,000, N = 5 years, and i = 7% • Find: A • Solution: A = $5,000(A/F,7%,5) = $869.50

  8. Example 2.10 Handling Time Shifts in a Uniform Series F = ? First deposit occurs at n = 0 i = 6% 0 1 2 3 4 5 $5,000 $5,000 $5,000 $5,000 $5,000

  9. Annuity Due • Excel Solution Beginning period =FV(6%,5,5000,0,1)

  10. Sinking Fund Factor F 0 1 2 3 N A Example 2.11 – College Savings Plan: • Given: F = $100,000, N = 8 years, and i = 7% • Find: A • Solution: A = $100,000(A/F,7%,8) = $9,746.78

  11. Excel Solution • Given: • F = $100,000 • i = 7% • N = 8 years • Find: • =PMT(i,N,pv,fv,type) • =PMT(7%,8,0,100000,0) • =$9,746.78

  12. Capital Recovery Factor P 1 2 3 0 N A = ? Example 2.12: Paying Off Education Loan • Given: P = $21,061.82, N = 5 years, and i = 6% • Find: A • Solution: A = $21,061.82(A/P,6%,5) = $5,000

  13. Example 2.14 Deferred Loan Repayment Plan P =$21,061.82 i = 6% 0 1 2 3 4 5 6 Grace period A A A A A P’ = $21,061.82(F/P, 6%, 1) i = 6% 0 1 2 3 4 5 6 A’ A’ A’ A’ A’

  14. Two-Step Procedure

  15. Present Worth of Annuity Series P = ? 1 2 3 0 N A Example 2.14:Powerball Lottery • Given: A = $7.92M, N = 25 years, and i = 8% • Find: P • Solution: P = $7.92M(P/A,8%,25) = $84.54M

  16. Excel Solution • Given: • A = $7.92M • i = 8% • N = 25 • Find: P =PV(8%,25,7.92,0) = $84.54M

  17. ? Option 1: Early Savings Plan 0 1 2 3 4 5 6 7 8 9 10 44 $2,000 Example 2.15 Early Savings Plan – 8% interest ? Option 2: Deferred Savings Plan 0 1 2 3 4 5 6 7 8 9 10 11 12 44 $2,000

  18. ? Option 1: Early Savings Plan 0 1 2 3 4 5 6 7 8 9 10 44 $2,000 Option 1 – Early Savings Plan Age 31 65

  19. ? Option 2: Deferred Savings Plan 0 11 12 44 $2,000 Option 2: Deferred Savings Plan

  20. At What Interest Rate These Two Options Would be Equivalent?

  21. Using Excel’s Goal Seek Function

  22. Result

  23. $396,644 Option 1: Early Savings Plan 0 1 2 3 4 5 6 7 8 9 10 44 $2,000 $317,253 Option 2: Deferred Savings Plan 0 1 2 3 4 5 6 7 8 9 10 11 12 44 $2,000

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