1. Engineering Economy IEN255 Chapter 3 Leftovers Commercial Loan Transactions  Amortized Loans  B n = Remaining Balance at the end of period n, with B 0 = P  I n = Interest payment in period n, where I n = B n-1 i  P n = Principle payment in period n.  So, each payment can be defined as: A = P n + I n

2. Engineering Economy Tabular Method  Tabular method (spreadsheet)  Interest at end of first period I 1 = B 0 i = P i  Principle Payment at end of first period P 1 = A - P i  Balance remaining after first payment B 1 = B 0 - P 1 = P - P 1  At the end of the second period ä I 2 = B 1 i = (P - P 1 )i ä P 2 = A - (P - P 1 )i = (A - P 1 i) + P 1 i = P 1 (1 +i) ä B 2 = B 1 - P 2 = P - (P 1 + P 2 ) ä and so on to page 146.

3. Engineering Economy Figure 3.18

4. Engineering Economy Remaining Balance Method  (3.15) B n = A (P/A, i, N - n) (balance)  (3.16) B n-1 i = A(P/A, i, N - n + 1) i (interest payment)  (3.17) P n = A(P/A, i, N - n + 1) (principle payment)  Figure 3.19

5. Engineering Economy Add on Loans  Simple Interest!!!  Precalculated interest and paid in equal installments  Quoted is add on rate (simple) ex - 12% 2 years  nominal is 21.60 %!  Effective is 23.87% !  Again, to find use linear interpolation

6. Engineering Economy Variable rate mortgages  mortgage - buying property  monthly rates  changing rate over time (rises a few years then fixes to a certain rate) or (tied to some index (T- Bills)  figure3.22

7. Engineering Economy Bond Terminology  Mortgage Bond - if default on bond, property backs bond  Debenture Bond - simply pledge overall assets  Par value - Face value (usually in even denominations (1000s))  Maturity date - Date Par value repaid  Coupon Rate - Interest rate paid (annual coupon rate)  Discount Bond - A bond that sells below par (face) value  Premium Bond - A bond that sells above par (face) value  Market Price - Value of the bond

8. Engineering Economy Figure 3.23

9. Engineering Economy Bond valuation  yield to maturity - interest rate of equivalence  future interest & face value receipts = market price  fig 3.24

10. Engineering Economy Interpolation to find interest rate  pg 159

11. Engineering Economy IEN255 Summer’99 Chapter 3 HW#2  Homework Assignment: Chapter 3 #’s 3.66; 3.73; 3.78  Due with chapter 4 homework (likely Tues June 29)