| Interest rates have fallen over the seven years since a $1,000 par, 10-year bond was issued with a coupon of 7%. What is the present value of this bond if the required rate of return is currently four and one-half percent? (For simplicity, assume annual payments.) 
 
 
 
 
Each of the remaining cash flows on the bond is discounted at the annual rate of 4.5%. 
| Period  | Payment  | Discount  | PV  |  
|  1  | $1,000 × 7% = $70  | (1.045)1  | $ 66.99  |  
|  2  | $1,000 × 7% = $70  | (1.045)2  | $ 64.10  |  
|  3  | $1,000 × 7% = $70  | (1.045)3  | $ 61.34  |  
|  3  | $1,000 principal  | (1.045)3  | $ 876.30  |  
| Total Present Value of Cash Flows  | $1,068.73  |  The present value can also be determined with a financial calculator. N = 3, I = 4.5%, PMT = $1,000 × 7%, FV = $1,000. Solve for PV = $1,068.724.  |