Most bonds offer coupons, or interest rates. When the bond matures, the investor receives interest in addition to the bond's face value. Non-interest bearing notes offer no such coupon, but they do offer returns. This is because investors buy them at a price significantly less than the bond's face value. The note then offers a fixed return rather than the risk or potential reward of varying market interest rates. Its imputed interest is the interest rate that would raise the note's discounted value to its face value by the note's maturity date.

Divide the note's face value buy its discounted price. For example, if you pay $4,000 for a $6,500 non-interest bearing note that matures in five years, divide $6,500 by $4,000, giving 1.625.

Divide 1 by the number of years until the bond matures. With this example, 1 divided by 5 is 0.2.

Raise the ratio from the first step to the power of the inverse value from the second step. Continuing the example, 1.625 raised to the power of 0.2 gives approximately 1.102.

Subtract 1, giving 0.102.

Multiply your answer by 100. With this example, this produces 10.2. This is the note's imputed interest rate.

#### References

- "Accounting Handbook"; Joel G. Siegel and Jae K. Shim; 2006
- "Investing in Zero Coupon Bondsâ€¦"; Lawrence R. Rosen; 1986

#### Resources

- "Introduction to Financial Accounting"; Charles T. Horngren, Ph.D.; 2008
- "Accounting for Investments…"; R. Venkata Subramani; 2011