Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $ 1 comma 000 , and a coupon rate of 7.4 % (annual payments). The yield to maturity on this bond when it was issued was 6.1 %. What was the price of this bond when it was issued?

What was the price of this bond when it was issued?

$ 1,095,23

Explanation:

To know the Price of the bond when it was issued we need first to calculate the Present Value of the Principal and then through the annuity method calculate the Present Value of the coupons.

Bond Value

Principal Present Value = F / (1 + r) ^t

Coupon Present Value = C x [1 - 1 / (1 + r) ^t] / r

The price of this bond it's $553 + $542 = $1,095,23

Bond $1,000

Coupon $74,00

Annual Rate 7,4%

YTM 6,1%

Years 10

Present Value of Bonds $553 = 1,000 / (1+0,061) ^10

Bond 1.000

YTM Rate 6,10%

Periods 10

Present Value of Coupons $542 = 74 (Coupon) x 7,33

7,33 = [1 - 1 / (1+0,061) ^10 ] / 0,061

Bond 1.000

YTM Rate 6,10%

Periods 10