# How is a bond with maturity valued?

There are basically three types of bonds in the market −

• Bonds with maturity
• Purely discount bonds
• Perpetual bonds.

In this article, we will see how the bonds with maturity are valued. Bonds with maturity have a maturity date on which the bond's value with the interest payment is returned to the investor.

Note − There are three types of bonds depending on their characteristics, but the bond with a maturity is the most common among them.

## Bonds with Maturity

Governments usually offer bonds that have a given interest rate and a maturity period. The net present value of a bond is its period of cash flows (discounted). That, in other words, can be written as annual interest plus the bond's maturity or terminal.

The discount rate in bonds with maturity is the interest rate that investors can obtain from similar bonds with similar characteristics. By comparing the bond's current market value and its present value investors can decide whether the bond is undervalued or it is overvalued.

Note − Bonds with maturity comes with great advantages for the investors. Apart from paying the interests due on each period, it offers the lumpsum back on maturity of the bond.

## Calculations

As in the case of bond with maturity, we can take it as an annuity (same amount of cash paid annually), we can use a simple formula like the one we used to calculate annuity.

$$Present\:Value = Present\:Value\:of \:interest + Present\:Value\:of\:maturity$$

$$B_{0} = \lbrace \frac{INT_{1}}{(1 + K_{d})}+\frac{INT_{2}}{(1 + K_{d})^2}+...+ \frac{INT_{n}}{(1 + K_{d})^n}\rbrace + \frac{B_{n}}{(1 + K_{d})^n}$$

$$B_{0} = \displaystyle\sum\limits_{n}^{𝑡=1} \frac{INT_{t}}{(1 + K_{d})^t}+\frac{B_{n}}{(1 + K_{d})^n}… … … … (1)$$

Where,

• B0 is the present value of a bond (debenture),

• Σ INTt shows the interest amount in period t (from year 1 to n),

• kd shows the market interest rate,

• Bn is bond’s maturity value or terminal in period n and n is the number of years to maturity.

It is important to note that in equation (1) the right hand portion shows the formula of an annuity for the total period of the bond and a final payment on the terminal of the annuity.

So, we can write,

$$B_{0} = INT × [\frac{1}{K_{d}}-\frac{1}{K_{d}(1 + K_{d})^n}]+\frac{B_{𝑛}}{(1 + K_{d})^𝑛}$$