Question

Bond Features
Maturity (years) =	7
Face Value =	$1,000
Starting Interest Rate	4.78%
Coupon Rate =	4%
Coupon dates (Annual)

If interest rates change from 4.78% to 5.02% immediately after you buy the bond today (and stay at the new interest rate), what is the price effect in year 5 ?

State your answer to the nearest penny (e.g., 48.45)

If there is a loss, state your answer with a negative sign (e.g., -52.30)

Answer 1

given information:

Face value = $1000

years(n) = 7 years

coupon Rate 4%

Coupon payment = 1000*4% =40

1) calculation of present value of bond when the intrest rate is 4.78 till the maturity of bond i.e. 7 years

Present value(Po)= ( Coupon payment (C) * PVIFA , interest rate (K), n) + ( Face value of bond (FV) * PVIF , K, n)

Po= ( 40 * 5.833, 4.78, 7years) + ( 1000 * 0.7212, 4.78 , 7years)

= 233.32 + 721.2

=954.52

2) calculation of present value of bond when the intrest rate is 5.02 till the maturity of bond i.e.7 years

Present value(Po)= ( C*PVIFA , K, n) + ( FV * PVIF , K, n)

Po= ( 40 * 5.782, 5.02, 7years) + ( 1000 * 0.7097, 5.02 , 7years)

= 231.28 + 709.7

=940.98

3) calculation of price effect on 5th year

years	cash flows	pv @ 4.78%	present value of cash flows @ 4.78% (A)	pv @ 5.02%	present value of cash flows @ 5.02% (B)	price difference (A-B)
1	40	0.954	38.16	0.952	38.08	0.08
2	40	0.911	36.44	0.907	36.28	0.16
3	40	0.869	34.76	0.863	34.52	0.24
4	40	0.829	33.16	0.822	32.88	0.28
5	40	0.792	31.68	0.783	31.32	0.36
6	40	0.756	30.24	0.745	29.8	0.44
7	1040	0.721	749.84	0.7097	738.09	11.75

Interest rate and price have inverse relationship when the intrest rate increase the value of bond decrease or people less willing to buy. from above example where increase in interest rate lead to decrease in the value of bond by 13.54 ( 954.52 - 940.98) .