Question

A $8,500 bond had a coupon rate of 4.50% with interest paid semi-annually. Ali purchased this bond when there were 9 years left to maturity and when the market interest rate was 4.75% compounded semi-annually. He held the bond for 3 years, then sold it when the market interest rate was 4.25% compounded semi-annually.

a. What was the purchase price of the bond?

Round to the nearest cent.

b. What was the selling price of the bond?

Round to the nearest cent.

c. What was Ali's gain or loss on this investment?

(click to select)Gain or Loss

amount was $ _____

.

Answer 1

a

Particulars	Cash flow	Discount factor	Discounted cash flow
present value Interest payments-Annuity (2.375%,18 periods)	$                       191.25	14.50928	$             2,774.90
Present value of bond face amount -Present value (2.375%,18 periods)	$                    8,500.00	0.65540	$             5,570.94
Bond price			$             8,345.84
Face value			$             8,500.00
Premium/(Discount)			$              (154.16)
Interest amount:
Face value	8,500
Coupon/stated Rate of interest	4.500%
Frequency of payment(once in)	6 months
Interest amount	8500*0.045*6/12=		$                191.25
Present value calculation:
yield to maturity/Effective rate	4.75%
Effective interest per period(i)	0.0475*6/12=		2.375%

Purchase price is

8,345.84

b

Particulars	Cash flow	Discount factor	Discounted cash flow
present value Interest payments-Annuity (2.125%,12 periods)	$                       191.25	10.49461	$             2,007.09
Present value of bond face amount -Present value (2.125%,12 periods)	$                    8,500.00	0.77699	$             6,604.41
Bond price			$             8,611.51
Face value			$             8,500.00
Premium/(Discount)			$                111.51
Interest amount:
Face value	8,500
Coupon/stated Rate of interest	4.500%
Frequency of payment(once in)	6 months
Interest amount	8500*0.045*6/12=		$                191.25
Present value calculation:
yield to maturity/Effective rate	4.25%
Effective interest per period(i)	0.0425*6/12=		2.125%

Selling price is

8,611.51

c

Gain on sale is 265.67