Question

Tina buys a 1000 par value 10-year bond with 10% annual coupons at a price to yield an annual effective rate of 10%. the coupons were reinvested at an annual effective rate of 8%. immediately after receiving the 4th coupon payment, tina sells the bond to joe for a price of p. p assumes an annual effective yield of i to the buyer. tina's annual effective yield from the date of purchase until the date of sale was 8%. calculate i

Answer 1

To calculate the yield to the new buyer, we must equate the present value of future cash flows from the bond, discounted at the desired annual effective yield rate i, with the sale price. Tina's yield is computed based on her initial investment and reinvestment rate of 8%. Time value of money concepts are key to solving for i.

Step-by-step explanation:

The question involves calculating the annual effective yield of Tina's investment in a bond until the sale, and finding the yield rate i for the new buyer, Joe. Tina bought a bond at an annual effective rate of 10% with 10% annual coupons and sold it after 4 years at an annual effective yield of her own of 8%. Considering the face value of the bond, the coupon rate, and the reinvestment rate, we can determine the price Tina sold the bond for and then calculate the yield rate i that Joe requires to make his investment desirable.

To solve for i, we can set up an equation where the present value of the future coupon payments and the face value redeemed at the end of the 10th year, discounted at Joe's required yield rate i, equals the price p that Tina sold the bond for. Tina's effective annual yield is calculated using the amount she invested and reinvested at 8% and comparing that to the total amount received when she sells the bond to Joe after the fourth coupon. Using time value of money principles, we solve for i that equates the present value of Joe's future cash flows from the bond to the price p.