Transparent method
The formula
Worked example
Example inputs
How to interpret the result
A bond's often-quoted yield to maturity assumes every coupon payment gets reinvested at that same yield the moment it's received, an assumption that rarely holds exactly in a changing rate environment. The realized return an investor actually earns depends heavily on what rates are actually available when each coupon comes in and needs to be reinvested.
Before you rely on it
What to check
Model a range of plausible reinvestment rates rather than assuming coupons always reinvest at the original yield to maturity.
The common error
Where people go wrong with bond coupon reinvestment calculator
Treating a bond's quoted yield to maturity as the return that's guaranteed to be realized regardless of future rates. That figure embeds a reinvestment assumption that real, changing interest rates rarely match exactly.
Sensitivity evidence
How face value changes the coupons plus reinvestment growth
| Face value | Coupons plus reinvestment growth | Reinvestment growth above coupons | Total maturity proceeds |
|---|---|---|---|
| $800 | $462 | $62 | $1,262 |
| $900 | $520 | $70 | $1,420 |
| $1,000worked example | $578 | $78 | $1,578 |
| $1,100 | $636 | $86 | $1,736 |
| $1,200 | $694 | $94 | $1,894 |
Every input, tested
Which input moves the coupons plus reinvestment growth most
| Input | Tested from | To | Coupons plus reinvestment growth at each end | Swing |
|---|---|---|---|---|
| Years to maturity | 7.0 years | 13.0 years | $386 to $788 | $402 (69%) |
| Annual coupon rate | 4.0% | 6.0% | $462 to $694 | $231 (40%) |
| Face value | $900 | $1,100 | $520 to $636 | $116 (20%) |
| Coupon reinvestment rate | 2.0% | 4.0% | $550 to $607 | $57 (9.9%) |
| Coupons per year | 1 | 3 | $573 to $580 | $6.55 (1.1%) |
Two variables at once
Coupons plus reinvestment growth by face value and annual coupon rate
| Face value \ Annual coupon rate | 3.0% | 5.0% | 7.0% |
|---|---|---|---|
| $800 | $277 | $462 | $647 |
| $900 | $312 | $520 | $728 |
| $1,000 | $347 | $578 | $809 |
| $1,100 | $382 | $636 | $890 |
| $1,200 | $416 | $694 | $971 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Face value | $1,000 |
| Annual coupon rate | 5.0% |
| Years to maturity | 10.0 years |
| Coupons per year | 2 |
| Coupon reinvestment rate | 3.0% |
| Coupons plus reinvestment growth | $578 |
| Reinvestment growth above coupons | $78 |
| Total maturity proceeds | $1,578 |
Where the inputs come from
Face value, annual coupon rate, years to maturity and coupons per year define the payments the bond makes. The coupon reinvestment rate is the return you assume on each coupon after receiving it, such as a savings or money-market rate, or the same bond's yield. Use a realistic reinvestment rate, which often differs from the original yield, and remember that reinvestment must be done in something safe to keep the assumption honest.
Using the coupons plus reinvestment growth in a real decision
If reinvestment rates fall, the return is lower than the yield to maturity promised.
When the result stops applying
The yield to maturity calculation silently assumes coupons are reinvested at the yield itself, which is rarely true, so the actual return is often lower or higher. Taxes on coupons reduce what is available to reinvest. The calculation is nominal and ignores inflation. Zero-coupon bonds avoid reinvestment risk because they pay no coupons.
What to compare it with
Compare with the yield to maturity calculator, which assumes reinvestment at the same rate, and see the zero-coupon bond page for a case with no reinvestment risk. The compound interest and future value calculators show reinvested growth in general. The bond ladder page reinvests maturing rungs.
People also ask
Frequently asked questions
What is reinvestment risk?
The chance that coupons, or a maturing bond's principal, must be reinvested at lower rates than the original yield, reducing the total return.
Why does YTM assume reinvestment at the same rate?
It is a mathematical feature of the calculation, so the realized return only equals YTM if coupons really are reinvested at that yield.
Which bonds have no reinvestment risk?
Zero-coupon bonds held to maturity, since there are no coupons to reinvest, though they have high price sensitivity to rates.