Question

Suppose that a $100 face value 10 year bond that has an annual 7% coupon and the market rate of interest is 6.5%. How much will the price of this bond change in percentage terms if the interest rate falls to 6.0%?

1. Increase by 3.64%

2. Increase by 5.00%

3. Increase by 3.54%

4. Decrease by 5.00%

Answer 1

Given about a bond,

Face value = $100

years to maturity = 10 years

coupon rate = 7% paid annually,

So, annual coupon payment = 7% of 100 = $7

Yield to maturity = 6.5%

So, current price of the bond can be calculated on financial calculator using following values:

FV = 100

N = 10

PMT = 7

I/Y = 6.5

Compute for PV, we get PV = -103.59

So, current price of the bond = $103.59

When interest rates fall to 6%

New YTM = 6%

use following values:

FV = 100

N = 10

PMT = 7

I/Y = 6

compute for PV, we get PV = -107.36

So new price of the bond = $107.36

So, percentage change in price = (new price - old price)/old price = (107.36-103.59)/103.59 = 3.64%

So, price of the bond increased by 3.64%

Option A is correct.