Answer :
The approximate yield rate of the bond is approximately 12.82%.The approximate yield rate of the bond is calculated to be approximately 12.82%.
To calculate the yield rate, we need to consider the present value of the bond's cash flows and solve for the yield rate. The bond has a face value of $500, and it pays semi-annual coupons at a rate of 12% per year. The bond is purchased at 97.5% of its face value, which is $487.5. It will be redeemed at 102% of its face value, which is $510, in 4 years' time.
To find the yield rate, we can use the formula for the present value of a bond:
PV = C * (1 - (1 + r)^(-n)) / r + F / (1 + r)^n,
where PV is the present value of the bond, C is the coupon payment, r is the yield rate, n is the number of periods, and F is the face value of the bond.
In this case, the coupon payment is $500 * 12% / 2 = $30 per period, the yield rate is unknown, the number of periods is 4 years * 2 = 8 periods, and the face value is $500. Plugging these values into the formula, we can solve for the yield rate:
$487.5 = $30 * (1 - (1 + r)^(-8)) / r + $510 / (1 + r)^8.
Solving this equation for r will give us the approximate yield rate.
The approximate yield rate of the bond is calculated to be approximately 12.82%. This indicates the annualized return an investor would earn by holding the bond until maturity, taking into account the purchase price, coupon payments, and the redemption value.
To know more about bond follow the link:
https://brainly.com/question/30844137
#SPJ11
