Question

A government issues $4000000 of serial bonds paying interest at j2 = 9%, of which $2000000 is redeemed in 10 years, $2000000 is redeemed in 15 years and $0 is redeemed in 20 years. Determine the purchase price on the day that the bonds were issued, in order for investors to receive a yield of j2 = 4%.

Answer 1

C = interest rate = $2,000,000 * 9% = $180,000

r = yeild rate = 4%

n1 = 10 years

n2 = 15 years

P1 = Redemption in 10 years = $2,000,0000

P2 = Redemption in 15 years = $2,000,0000

Purchase Price =[[C * [1 - (1+r)^-n1] / r] + [[C * [1 - (1+r)^-n2] / r] + [P1 / (1+r)^n1] + [P2 / (1+r)^n2]

= [[$180,000 * [1 - (1+4%)&^-10] / 4%] + [[$180,000 * [1 - (1+4%)&^-15] / 4%] + [$2,000,000 / (1+4%)^10] + [$2,000,000 / (1+4%)^15]

= [$180,000 * 0.324435831 / 0.04] + [$180,000 * 0.444735497 / 0.04] + [$2,000,000 / 1.48024428] + [$2,000,000 / 1.80094351]

= $1,459,961.24 + $2,001,309.74 + $1,351,128.34 + $1,110,529

= $5,922.928.32

Therefore, Purchase price of bond can be $5,922,928.32