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 = = 1060$ The interest earned during the second 6 months = 1060×0.06 = 63.6$ Total interest earned during the year = = 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,