Question

Consider a 10 year bond with a coupon rate of 7% and annual coupon payments. Draw a graph showing the relationship between the price and the interest on this bond. The price should be on the y-axis and the interest rate on the x-axis. To compute the various prices, consider interest rates between 2% and 12% (use 0.5% increments). So your x-axis should go from 2%, then 2.5% … until 11.5% and then 12%. Is the relationship linear (i.e. is the slope constant)? Start at 7%. If interest rates go up or down by 0.5% is the price changing by the same amount? What type of relationship do we observe between prices and interest rates (liner, concave, convex or something else)?

No Chart

Answer 1

1.

Interest Rate	Price
2.00%	$1,449.13
2.50%	$1,393.84
3.00%	$1,341.21
3.50%	$1,291.08
4.00%	$1,243.33
4.50%	$1,197.82
5.00%	$1,154.43
5.50%	$1,113.06
6.00%	$1,073.60
6.50%	$1,035.94
7.00%	$1,000.00
7.50%	$965.68
8.00%	$932.90
8.50%	$901.58
9.00%	$871.65
9.50%	$843.03
10.00%	$815.66
10.50%	$789.48
11.00%	$764.43
11.50%	$740.45
12.00%	$717.49

No, the relationship is not linear i.e., the slope is not constant

No the price changes by different amount

Convex relationship