Question

A twelve year 5,000 par valued floating rate bond with annual coupons has a price P such that the investor’s APY is 8%. The annual coupon rate for the n-th year is given by the function .07+.0035*n (please no excel formulas)

a. Find the price P

b. Find the amount of Principal P6 in the sixth coupon payment

c. Find the interest I5 in the fifth coupon payment

d. Find the amount of the discount or premium for this bond.

Answer 1

Year	Coupon Rate			Cash Flow [5000*coupon rate]	Discounting Factor [1/(1.08^year)]	Present Value [cash flows* discounting factor]	Year	Discounting Factor [1/(1.08^year)]	Present Value [cash flows* discounting factor]
1	0.07+(0.0035*	1)=	0.0735	367.5	0.925925926	340.2777778
2	0.07+(0.0035*	2)=	0.077	385	0.85733882	330.0754458
3	0.07+(0.0035*	3)=	0.0805	402.5	0.793832241	319.517477
4	0.07+(0.0035*	4)=	0.084	420	0.735029853	308.7125382
5	0.07+(0.0035*	5)=	0.0875	437.5	0.680583197	297.7551487
6	0.07+(0.0035*	6)=	0.091	455	0.630169627	286.7271802	1	0.925925926	421.2962963
7	0.07+(0.0035*	7)=	0.0945	472.5	0.583490395	275.6992118	2	0.85733882	405.0925926
8	0.07+(0.0035*	8)=	0.098	490	0.540268885	264.7317534	3	0.793832241	388.9777981
9	0.07+(0.0035*	9)=	0.1015	507.5	0.500248967	253.8763508	4	0.735029853	373.0276503
10	0.07+(0.0035*	10)=	0.105	525	0.463193488	243.1765812	5	0.680583197	357.3061784
11	0.07+(0.0035*	11)=	0.1085	542.5	0.428882859	232.6689512	6	0.630169627	341.8670226
12	0.07+(0.0035*	12)=	0.112	560	0.397113759	222.3837048	7	0.583490395	326.7546213
12				5000	0.397113759	1985.568793	7	0.583490395	2917.451976
					Price P = (Sum of above PVs)	5361.170914	Principal Value in 6th coupon payment (Sum of above PVs)		5531.774136

I5 = 437.5

Premium = Price P - Par Value = 5361.17-5000 = 361.17

(If this was helpful then please rate positively. Thank You:)