# How do you calculate the actual or real interest rate on a bond investment?

## Definition of Actual or Real Interest Rate on a Bond Investment

The actual or real interest rate on a bond payable is also known as effective interest rate, yield to maturity, yield, and market interest rate. This rate can be calculated by discounting the bond's future cash amounts (semiannual interest payments and the maturity amount) back to the amount of cash paid to buy the bond (the present value).

## Example of Actual or Real Interest Rate on a Bond Investment

Assume an investor can purchase a \$300,000 7% bond that matures 5 years later for \$287,832. The investor will receive the following cash flows: semiannual interest of \$10,500 at the end of each of the 10 six-month periods + \$300,000 at the end of the 10th six-month period.

The actual interest rate to be earned by the investor (the bond's yield to maturity) is the interest rate that will discount the interest stream (an ordinary annuity) and the maturity amount (a lump sum) to \$287,832. This can be done with software, a financial calculator, or via trial and error using present value tables. In our example, the actual interest rate earned by the investor is 4% per semiannual period or 8% annually.

The reason that the bond can be purchased at a discount from its face and maturity amount, is that the current market interest rate is now 8% and the bond is paying only 7%. Because the market interest rate is more than the bond's stated interest rate, the market value of the bond is less than the maturity amount.