Question

A $5,000 bond with a coupon rate of 5.4​% paid semiannually has eight years to maturity and a yield to maturity of 6.5​%.

If interest rates fall and the yield to maturity decreases by​ 0.8%, what will happen to the price of the​ bond?

A.

rise by $ 243.62

B.

rise by $ 341.07

C.

fall by $ 243.62

D.

fall by $ 292.35

Answer 1

Interest rate = 6.5%:

Coupon = (0.054 * 5000) / 2 = 135

Number of periods = 8 * 2 = 16

Rate = 6.5% / 2 = 3.25

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 135 * [1 - 1 / (1 + 0.0325)¹⁶] / 0.0325 + 5000 / (1 + 0.0325)¹⁶

Price = 135 * [1 - 0.599458] / 0.0325 + 2,997.291893

Price = 135 * 12.324369 + 2,997.291893

Price = $4,661.081739

Interest rate = 6.5% - 0.8% = 5.7%:

Coupon = (0.054 * 5000) / 2 = 135

Number of periods = 8 * 2 = 16

Rate = 5.7% / 2 = 2.85

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 135 * [1 - 1 / (1 + 0.0285)¹⁶] / 0.0285 + 5000 / (1 + 0.0285)¹⁶

Price = 135 * [1 - 0.637869] / 0.0285 + 3189.343291

Price = 135 * 12.706363 + 3189.343291

Price = $4,904.702279

Change in price = $4,904.702279 - $4,661.081739

Change in price = $243.62

rise by $ 243.62