Question

Tram buys a $1000 bond with 5.9% annual coupons maturing at $1110. Find Tram's purchase price if the effective annual yield rate is 8% and the PV of the redemption value is $1027.78.

А. 1064.78
B. 1072.31
C. 1079.25
D. 1082.41
E. 1091.65

Answer 1

To find Tram's purchase price, we can calculate the present value (PV) of the bond using the effective annual yield rate and the PV of the coupons and the redemption value should be equal to the purchase price. Option E is corrrect.

Step-by-step explanation:

To find Tram's purchase price, we can calculate the present value (PV) of the bond using the effective annual yield rate. The present value of the coupons and the redemption value should be equal to the purchase price.

Let's calculate the present value of the coupons:

PV of coupons = ($1000 x 0.059) x (1 - (1 + 0.08)-2)/0.08 = $1110

Next, let's calculate the present value of the redemption value:

PV of redemption value = $1027.78

Finally, the purchase price is the sum of the present value of the coupons and the present value of the redemption value:

Purchase price = (PV of coupons) + (PV of redemption value) = $1110 + $1027.78 = $2137.78

Therefore, the correct answer is option E. 1091.65