# Interest Rates and Bond Prices: Exploring the Relationship

1. What is the present value of the bond? 2. How will the bond price be affected if the interest rate increases to 6%?

1. To compute the present value (PV) of the bond, we need to discount the future cash flows to their present values. The annual coupons of 805 can be considered as an annuity, and the face value of 1.0005 can be treated as a single payment. Using the formula for present value of an annuity and single payment, we can calculate the PV of the bond to be approximately 755.943. 2. If the interest rate increases to 6%, the bond price will decrease due to the inverse relationship between interest rates and bond prices. When the interest rate rises, the present value of future cash flows decreases, making the fixed cash flows of the bond less attractive compared to other investments offering higher rates. This causes investors to demand a lower price for the bond, resulting in a decrease in its price.

## Calculating the Present Value of the Bond

**Annual coupons:** 805

**Face Value:** 1.0005

**Annual Interest rate:** 6%

To find the present value (PV) of the bond, we calculate the present value of the annual coupons and face value separately.

## Present Value of Coupons:

Using the formula for present value of an annuity:

PV of coupons = 805 * (1 - (1 + 0.06)^(-1)) / 0.06

PV of coupons ≈ 755

## Present Value of Face Value:

Using the formula for present value of a single payment:

PV of face value = 1.0005 / (1 + 0.06) ≈ 0.943

Therefore, the PV of the bond is calculated by summing up the PV of coupons and the PV of face value:

PV of bond ≈ 755 + 0.943 ≈ 755.943

## Impact of Increased Interest Rate:

When the interest rate increases to 6%, the bond price will decrease. This is because higher interest rates reduce the present value of future cash flows, making the bond less attractive to investors who seek higher returns. As a result, the bond price will decrease to align with the market's interest rate expectations.