Answer:
- a. What will be the price of each bond if their yields increase to 7.8%?
4 Years : $966,73 (see example)
8 Years : $942,09
30 Years : $885,26
- b. What will be the price of each bond if their yields decrease to 5.8%?
4 Years : $1,034.81 (see example)
8 Years : $1,062.59
30 Years : $1,140.64
Explanation:
Principal Present Value = F / (1 + r)^t
Coupon Present Value = C x [1 - 1/(1 +r)^t] / r
This is an example for 4 years, 7,8%, to the others years only change "t".
The price of this bond it's $740,50 + $226,23 = $966,73
Present Value of Bonds $740,50 = $1,000/(1+0,0780)^4
Present Value of Coupons $226,23 = $68 (Coupon) x 3,33
3,33 = [1 - 1/(1+0,0780)^4 ]/ 0,0780
This is an example for 4 years, 5,8%, to the others years only change "t".
The price of this bond it's $798,10 + $236,71 = $1,034.81
Present Value of Bonds $798,10 = $1,000/(1+0,0580)^4
Present Value of Coupons $236,71 = $68 (Coupon) x 3,48
3,48 = [1 - 1/(1+0,0580)^4 ]/ 0,0580
