Last year,Danielle bought a bond for $10,000 that promises to pay $1,150 a year.This year,a person who buys a bond for $10,000 receives $1,210 a year.If Danielle were to sell her (old)bond,its price would be approximately

Question

Quizplus · Accepted Answer

The value of a bond is directly proportional to its annual yield. As the yield on the newly issued bond is higher than what Danielle holds, the value of her bond will decrease to adjust for the lower yield. We can use the formula for present value of a bond to determine the approximate price at which Danielle can sell her old bond:

PV = C / r * (1 - 1/(1+r)^n)

where PV is the present value, C is the annual coupon payment, r is the yield or interest rate, and n is the number of years.

For Danielle's bond, C = $1,150, r = 0.115 (since she gets $1,150 from a $10,000 investment), and n = 1. Plugging these values into the formula, we get:

PV = $1,150 / 0.115 * (1 - 1/(1+0.115)^1) = $9,504.35

Therefore, Danielle can sell her old bond for approximately $9,504. This is lower than the face value of $10,000 because the yield on the newly issued bond is higher.

Last Year,Danielle Bought a Bond for $10,000 That Promises to Pay