Question

Eric bought a $5,000 Bond today with a coupon rate of 2% for quarter payable quarterly. he will redeem it at maturity in four years from now which of the following calculations is correct if Eric wants to have a rate of return of 6% for quarter where X is used if you don't know the value and P represents the purchase price. No excel please.

P = $5,000(0.02)(PIA 6%, 4) + $X(P|F 6%, 4) P = $5,000(0.06)(PIA 2%, 4)+ $5,000(PIF 2%, 4) P = $5,000(0.02)(P|A 6%, 16) + $5,000(P|F6%, 16) P = $5,000(0.06)(P|A6%, 16) + $X(PIF6%, 16)

Answer 1

The correct calculation is

P = 5,000*(0.02)(P/A, 6%, 16) + 5,000*(P/F, 6%, 16)

Current bond price is the sum of the present values of all coupon payments and par value at maturity.

Coupon payment = par value*rate = 5,000*2% = 100.

There are 16 coupon payments so the PV of the coupon payments is given by 5,000*0.02*(P/A, 6%, 16) which is

100*((1+6%)^16 -1)/(6%*(1+6%)^16) = 1,010.59

Present value of par value at maturity = 5,000*(P/F, 6%, 16) = 5,000/(1+6%)^16 = 1,968.23

Price P = 1,010.59 + 1,968.23 = 2,978.82