How to use the bond total return calculator
The calculator starts with an example: a 10-year bond with a 4.5% coupon bought at $960 and sold after 5 years. Replace the figures with your own bond.
- Purchase price and face value. Enter the price per bond in dollars, without accrued interest. A US corporate or Treasury bond quoted at 96 per 100 costs $960 per $1,000 of face value.
- Coupon rate and frequency. Most US bonds pay twice a year.
- Years to maturity and holding period. If the holding period equals the years to maturity, the bond is redeemed at face value and the sale inputs are ignored.
- Reinvestment rate. The rate you expect to earn on coupons until the end, for example a money market or savings rate.
- Sale price. Enter the price directly, or enter the market yield you expect at the time of sale and the calculator prices the bond for the years it has left.
The chart stacks the three sources of return year by year, and the table shows coupons, interest on interest and the reinvested balance for each year.
How total return is calculated
Coupons are reinvested at the reinvestment rate, compounded once per coupon period, until the end of the holding period:
Interest on interest = Future value of coupons − n × C
Total return = Future value of coupons + Sale price − Purchase priceC is the coupon per period (face × coupon rate ÷ f), i the reinvestment rate ÷ f, n the number of coupons received and f the number of coupons a year.
The annualized figures turn the ending value into a yearly rate:
Bond-equivalent horizon return = f × [(Ending value ÷ Purchase price)1/n − 1]Ending value = future value of coupons + sale price. The bond-equivalent figure uses the same convention as a quoted yield to maturity, so the two are comparable.
When you enter a yield at sale, the sale price is the present value of the remaining coupons and the face value at that yield, the standard bond price formula from our bond price calculator.
A worked example
You buy a bond with a 4.5% semiannual coupon and 10 years to maturity for $960. At that price its yield to maturity is 5.01%.
Over 5 years you collect $225.00 in coupons. Reinvested at 4%, they earn another $21.37 of interest on interest.
You then sell when bonds with five years left yield 4.75%. The bond fetches $988.99, a capital gain of $28.99.
The total return is $275.36, or +28.68% over five years: +5.17% a year. On the bond-equivalent basis that is 5.11%, slightly above the yield you bought at, because the bond sold at a lower yield than you paid for.
Why your return differs from the yield to maturity
The yield to maturity at purchase assumes three things: you hold to maturity, every payment arrives on time, and every coupon is reinvested at that same yield. Change any of them and the return changes. The sale yield matters most over a short holding period:
| Yield when you sell after 5 years | Sale price | Total return | Annualized |
|---|---|---|---|
| 3.5% (rates fell) | $1,045.51 | $331.87 | +6.12% |
| 4.75% | $988.99 | $275.36 | +5.17% |
| 6% (rates rose) | $936.02 | $222.39 | +4.26% |
The same bond earns anywhere from +4.26% to +6.12% a year depending on where rates stand on the day you sell. This is interest rate risk in practice, and it grows with the years the bond has left at the time of sale; the bond duration calculator measures it.
Reinvestment risk when you hold to maturity
Holding to maturity removes the price risk, since you receive the face value, but the reinvestment rate still matters:
| Coupons reinvested at | Interest on interest | Total return over 10 years | Annualized |
|---|---|---|---|
| 2% | $45.43 | $535.43 | +4.53% |
| 4% | $96.69 | $586.69 | +4.88% |
| 6% | $154.58 | $644.58 | +5.27% |
Only if every coupon were reinvested at exactly the purchase yield of 5.01% would the bond-equivalent horizon return equal it. The effect grows with the coupon and the maturity: interest on interest is a large part of the return on long, high-coupon bonds and nothing at all on a zero-coupon bond, which locks in its yield exactly if held to maturity.
The two risks pull in opposite directions. When rates rise, the bond’s price falls but coupons are reinvested at higher rates; when rates fall, the price rises but reinvestment earns less. Over a holding period close to the bond’s duration, the two effects roughly offset, which is the idea behind immunization in bond portfolio management.
Reading the result
- Use the annualized return to compare. A +61.11% total return over ten years and a +28.68% return over five are not comparable until both are annualized.
- Check the share of the price change. In the example the sale contributes 11% of the total return. A result that depends heavily on selling at a lower yield is a bet on rates, not income.
- Compare with the purchase yield. The bond yield calculator gives the yield to maturity and current yield for any price; this page shows how far a realistic holding period can drift from it.
What this calculator does not include
- Accrued interest and settlement dates. The bond is assumed to be bought and sold on coupon dates. Between coupon dates the buyer also pays accrued interest, which the seller receives.
- Taxes and trading costs. Coupons are usually taxed as ordinary income in the US, and bid-ask spreads on individual bonds can be wide for small trades.
- Default, calls and sinking funds. A callable bond may be redeemed early, usually when rates have fallen and reinvestment is least attractive.
- A changing reinvestment rate. One rate applies to every coupon. In reality, the rate you earn on coupons moves with the market.