## Determine ytm price formula, Basic Statistics

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YTM can be determined using the price formula of a bond.

Part a

The present value (price) formula for a zero coupon bond is:

PV = F/(1+i)n

Plugging in the given information,

\$300 = \$1000/(1+i)15

(1+i)15 = 3.33

1+i = 1.08357

i = YTM = 0.08357 = 8.36%

Thus the YTM of the fifteen-yr zero coupon bond is 8.36%.

Part b

Semiannual coupon = 6%*\$500/2 = \$15

Plugging in the given information,

Price = \$15/(1+(i/2)) + \$15/(1+(i/2))2 +..... + \$15/(1+(i/2)6 + \$500/(1+(i/2)6 = \$400

On trial and error using Excel, YTM has been determined to be 7.23%.

Thus the YTM of the three-yr semiannually 6% coupon bond is 14.45%.

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