According to the formula,

Bond price= y/r
so bond price has a inverse relationship with interest rate.i.e. interest rate increases, bond price decreases.
But why does it contradict with this demand-supply anysis: r(interest rate increases)--> returns from buying bonds increase-->cost of holding money increases-->asset demand for money decrease-->supply of bonds decreases-->PRICE OF BONDS INCREASES

what's wrong with the demand-supply anysis, thx!

My logical deduction is: asset demand for money + transaction demand for money= money demand=supply of bond(as bond issuers create supply of bonds)

Because bonds are typically sold with fixed denominations at a set interest rate; say $10,000 at 6%. If interest rates are 6% and the bond pays 6%, then the bond is being sold at par or $10,000. Now say the interest rates rise to 7%. You certainly wouldnt pay 10,000 for the bond. You buy at discount and pay something less.

The equation you provided, Bond price = yield/interest rate (or y/r), is a simplified version of the relationship between bond prices and interest rates. In reality, the relationship between bond prices and interest rates is more complex and involves factors such as time to maturity, coupon payments, and the market's expectation of future interest rates.

In your first statement, you correctly pointed out that bond prices have an inverse relationship with interest rates. This means that as interest rates rise, bond prices tend to decrease, and vice versa. This relationship is based on a fundamental principle in finance called the time value of money. When interest rates rise, the yield or return that investors can earn from other investments also increases. As a result, the value of existing bonds with fixed interest rates becomes less attractive to investors, leading to a decrease in their prices.

Now, let's discuss your second statement, which highlights the demand-supply analysis. The demand-supply analysis considers the effect of an increase in interest rates on both the demand for and supply of bonds. When interest rates increase, the returns from buying bonds also increase. This implies that investors may find bonds more attractive as their potential to earn higher returns grows. As a result, the demand for bonds might increase.

Simultaneously, an increase in interest rates also makes it more expensive to hold money. This means the cost of not investing in bonds becomes relatively higher compared to holding cash. Consequently, the demand for other assets, such as money, may decrease, while the supply of bonds may also decrease. This decrease in the supply of bonds could potentially drive up their prices.

So, while bond prices generally have an inverse relationship with interest rates, the demand-supply analysis suggests that both the demand for and supply of bonds can be influenced by interest rate movements, leading to potential deviations from the simple inverse relationship.

It is important to note that the relationship between bond prices and interest rates is influenced by several factors and can be subject to market dynamics, investor expectations, and various economic conditions. It is not always a straightforward cause-and-effect relationship, which can sometimes lead to observed inconsistencies or complex relationships between bond prices and interest rates.