Bonds and interest rates are inversely proportional

Lets understand a relation between bonds and interest rates. Suppose a investor has 2 choices to invest : 

1. A Govt backed bond

2. Govt zero

So in both case, risk factor is same, as issuer is same i.e. government and assume that returns are the same. Let the first bond pays 5% return and govt. bond's face value is Rs. 100.

So calculate the discounted value of zero.

So solution as both bond return the same, assume that P be the discounted value. 

So 100 = P+5% of P

P=100/105*100=95.23

Now suppose that return increases to 10% , the P = 100/110*100 =90.9

If suppose return decreases to 2% , P = (100/102)*100 = 98.40 .

So clearly we can infer:

Price is inversely proportional to interest rates