1. Interest Formulas – Equal Payment Series Lecture No.5 Professor C. S. Park Fundamentals of Engineering Economics Copyright © 2005

2. Equal Payment Series 012 N 0 12N AAA F P 0 N

3. Equal Payment Series – Compound Amount Factor 012 N 0 12N AAA F 012 N AAA F

4. Compound Amount Factor 012 N 0 12N AAA F A(1+i) N-1 A(1+i) N-2

5. Equal Payment Series Compound Amount Factor ( Future Value of an annuity) 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 0 1 2 3 N F A

6. Validation

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

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

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

10. Sinking Fund Factor 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 0 1 2 3 N F A

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 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 1 2 3 N P A = ? 0

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

14. Two-Step Procedure

15. Present Worth of Annuity Series 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 1 2 3 N P = ? A 0

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

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

18. Option 1 – Early Savings Plan 0 1 2 3 4 5 6 7 8 9 10 44 Option 1: Early Savings Plan $2,000 ? 6531Age

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

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

22. Using Excel’s Goal Seek Function

23. Result

25. 0 1 2 3 4 5 6 7 8 9 10 44 0 1 2 3 4 5 6 7 8 9 10 11 12 44 Option 1: Early Savings Plan Option 2: Deferred Savings Plan $2,000 $396,644 $317,253