Question

Helen purchased a $1,500 bond that was paying a coupon rate of 5.20% compounded semi-annually and had 5 more years to mature. The yield at the time of purchase was 6.70% compounded semi-annually.

a. How much did Helen pay for the bond?

Round to the nearest cent

b. What was the amount of premium or discount on the bond?

(click to select)PremiumDiscount

amount was

Round to the nearest cent

Answer 1

a.Information provided:

Future value (FV)= $1,500

Time (N)= 5 years*2= 10 semi-annual periods

Coupon rate= 5.20%/2= 2.60% per semi-annual period

Coupon payment= 0.026*1,000= $26 per semi-annual period

Yield to maturity (I/Y)= 6.7%/2= 3.35% per semi-annual period

The question is solved by calculating the present value.

The present value of the bond is calculated by entering the below in a financial calculator:

FV= 1,500

N= 10

PMT= 26

I/Y= 3.35

Press the CPT key and PV to compute the present value.

The value obtained is 1,296.79.

Therefore, Helen paid $1,296.79 for the bond.

b.It is a discount rate since the market value of the bond is lower than the purchase price of the bond.

Discount= $1,500 - $1,296.79

= $203.21.