Summary of Interest Formula Relationships of Discrete Compounding
- Slides: 25
Summary of Interest Formula
Relationships of Discrete Compounding
Deferred Annuity • Deferred annuities are uniform series that do not begin until some time in the future. • If the annuity is deferred J periods then the first payment (cash flow) begins at the end of period J+1.
Multiple Interest Formula
Interest Rate that Vary with Time
Nominal and Effective Interest Rate • The annual rate is known as a nominal rate. • A nominal rate of 12%, compounded monthly, means an interest of 1% (12%/12) would accrue each month, and the annual rate would be effectively somewhat greater than 12%. Consider a principal amount of 1000$ to be invested for a year at a nominal rate 12% compounded semiannually. Interest rate = 6% per 6 months. The interest earned during the first 6 months = 1000× 0. 06 = 60$ Total interest and principal at 6 months = 1000+60 = 1060$ The interest earned during the second 6 months = 1060× 0. 06 = 63. 6$ Total interest earned during the year = 60+63. 6 = 123. 6$ Effective annual interest rate = 123. 6/1000 = 12. 36%
M is the number of compounding interest per year i is effective interest rate per year r is the nominal interest rate per year
Compounding More Often than Once per Year
Example: A loan of 15, 000$ requires monthly payments of 477$ over a 36 month period of time. These payments include both principal and interest. 1. What is the nominal interest rate? nominal interest rate = 0. 75 × 12 = 9% 2. What is the effective interest rate per year
3. Determine the amount of unpaid loan principle after 20 month?
Interest Formulas for Continuous Compounding and Discrete Cash Flows • Interest is typically compounded at the end of discrete periods. • We can allow compounding to occur continuously throughout the period. • Continuous compounding assumes that cash flows occurs at discrete intervals, but that compounding is continuous throughout the interval.
Chapter 4 Home Work: 1, 3, 5, 7, 8, 10, 12, 14, 18, 20, 22, 25, 31, 34, 38, 47, 49, 54, 55, 60, 62, 64, 66, 68, 72, 95, 99, 100, 103, 107, 112, 113, 115, 116,