Investment Theory and Risk Management, + Website

General Pricing Formulas for Finite Cash Flow Streams

Again, assume the bond pays a coupon C for a definite period, n, as in:

Solving this finite power series yields

See Appendix 2.1 for the complete derivation. Suppose C stands for any payment (like a payment on an installment loan). It has no terminal face value, so we set M to zero. Then if P represents the loan amount, C (the payment) can be solved for as:

This is an amortization formula that gives the pay down on a loan over time n at interest rate r for n periods with principal P. It is of interest to amortize a loan into interest and principal payments.

Example 2.2

This example calculates the amortization schedule for each year in a 10-year loan with annual payments on a principal of $1,000 and interest rate equal to 10 percent.

This example clearly separates the principal and interest payments on the loan—the total payments equal $1,627.45, of which $1,000 is on the original principal, while $627.45 goes to interest. Extending this example, suppose that you are interested in buying a home with price P and mortgage rate r that will be financed over a 30-year period with monthly mortgage payments each equal to C. Then the ...