Final answer:
The current price of a two-year, $1,000 bond with a 3% interest rate is $1,028.26. If the interest rate increases to 6%, the price drops to $981.19. This change occurs because the present value of future cash flows decreases with higher discount rates.
Step-by-step explanation:
To find the current price of a two-year, $1,000 bond with annual coupon payments of $50 and a market interest rate of 3%, we would use the following formula:
Price = (C1 / (1 + r)) + (C2 + P) / (1 + r)^2
Where C1 is the first coupon payment, C2 is the second coupon payment, P is the principal amount of the bond (face value), and r is the market interest rate.
So, plugging the numbers in:
Price = (50 / (1 + 0.03)) + (50 + 1,000) / (1 + 0.03)^2 = $1028.26
Now if the interest rate increases to 6%, the formula would look like this:
Price = (50 / (1 + 0.06)) + (50 + 1,000) / (1 + 0.06)^2 = $981.19
Conceptually, the bond's price decreases when the interest rate increases because future cash flows are discounted at a higher rate, reducing their present value. When market interest rates go up, new bonds are issued at higher rates, making existing bonds with lower rates less attractive, thus their price drops to adjust for the yield difference.