INTEREST RATE SENSITIVITY An investor purchased the following S bonds. Each bond

Question

INTEREST RATE SENSITIVITY An investor purchased the following S bonds. Each bond had a par value of $1,000 and an 10% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell, and each then had a new YTM of price for each bond after the decline in interest rates? Fil n the following table. Round your answers to the n 7%, what is the percentage change in earest cent or to two decimal places. Enter all amounts as positive numbers. Price @ 10% Price @ 7% Percentage Change 5 3 508.35 10-year, 10% annual coupon 10-year zero 5-year zero 30-year zero $100 perpetuity s 508.35 751.38 1000 1000

Explanation / Answer

Price at 10%

Price at 7%

Percentage change

1-

10 Years 10% annual coupon

Using Present value function in MS excel

PV(10%,10,100,1000,0)

($1,000.00)

PV(7%,10,100,1000,0)

($1,210.71)

(1210.71-1000)/1000

21.07%

2-

10 Years Zero

Face value/(1+r)^n

1000/(1.1)^10

385.54329

1000/(1.07)^10

508.34929

(508.35-385.54)/385.54

31.85%

3-

5 Years Zero

Face value/(1+r)^n

1000/(1.1)^5

620.92132

1000/(1.07)^5

712.98618

(712.99-620.92)/620.92

14.83%

4-

30 Year zero

Face value/(1+r)^n

1000/(1.1)^30

57.308553

1000/(1.07)^30

131.36712

(131.37-57.30)/57.31

129%

Price at 10%

Price at 7%

Percentage change

1-

10 Years 10% annual coupon

Using Present value function in MS excel

PV(10%,10,100,1000,0)

($1,000.00)

PV(7%,10,100,1000,0)

($1,210.71)

(1210.71-1000)/1000

21.07%

2-

10 Years Zero

Face value/(1+r)^n

1000/(1.1)^10

385.54329

1000/(1.07)^10

508.34929

(508.35-385.54)/385.54

31.85%

3-

5 Years Zero

Face value/(1+r)^n

1000/(1.1)^5

620.92132

1000/(1.07)^5

712.98618

(712.99-620.92)/620.92

14.83%

4-

30 Year zero

Face value/(1+r)^n

1000/(1.1)^30

57.308553

1000/(1.07)^30

131.36712

(131.37-57.30)/57.31

129%

5-

100 perpetuity

perpetuity/rate

100/10%

1000

100/7%

1428.5714

(1428.57-1000)/1000

42.86%

5-

100 perpetuity

perpetuity/rate

100/10%

1000

100/7%

1428.5714

(1428.57-1000)/1000

42.86%

Price at 10%

Price at 7%

Percentage change

1-

10 Years 10% annual coupon

Using Present value function in MS excel

PV(10%,10,100,1000,0)

($1,000.00)

PV(7%,10,100,1000,0)

($1,210.71)

(1210.71-1000)/1000

21.07%

2-

10 Years Zero

Face value/(1+r)^n

1000/(1.1)^10

385.54329

1000/(1.07)^10

508.34929

(508.35-385.54)/385.54

31.85%

3-

5 Years Zero

Face value/(1+r)^n

1000/(1.1)^5

620.92132

1000/(1.07)^5

712.98618

(712.99-620.92)/620.92

14.83%

4-

30 Year zero

Face value/(1+r)^n

1000/(1.1)^30

57.308553

1000/(1.07)^30

131.36712

(131.37-57.30)/57.31

129%

Price at 10%

Price at 7%

Percentage change

1-

10 Years 10% annual coupon

Using Present value function in MS excel

PV(10%,10,100,1000,0)

($1,000.00)

PV(7%,10,100,1000,0)

($1,210.71)

(1210.71-1000)/1000

21.07%

2-

10 Years Zero

Face value/(1+r)^n

1000/(1.1)^10

385.54329

1000/(1.07)^10

508.34929

(508.35-385.54)/385.54

31.85%

3-

5 Years Zero

Face value/(1+r)^n

1000/(1.1)^5

620.92132

1000/(1.07)^5

712.98618

(712.99-620.92)/620.92

14.83%

4-

30 Year zero

Face value/(1+r)^n

1000/(1.1)^30

57.308553

1000/(1.07)^30

131.36712

(131.37-57.30)/57.31

129%

5-

100 perpetuity

perpetuity/rate

100/10%

1000

100/7%

1428.5714

(1428.57-1000)/1000

42.86%

5-

100 perpetuity

perpetuity/rate

100/10%

1000

100/7%

1428.5714

(1428.57-1000)/1000

42.86%

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