Discounting a Zero-Coupon Bond with a 30/360 Day Count

Summary

The document asks how to discount a single zero-coupon bond using a 30/360 day-count convention. It specifies start and end dates, a discount rate, and a redemption value, then gives a discount-factor expression based on the rate and elapsed time. The answer states that the dates correspond to 2,346 days under the stated convention and reports an approximate discount factor and present value for the cash flow.

This is a compact worked illustration of converting a day-count interval into a discount factor and applying it to a single payment. It does not explain the convention’s date-adjustment rules or show the day-count calculation in detail. The printed formula’s exponent and rate scaling may also depend on how the rate is compounded and how time is measured, so the numerical result should be interpreted in the context of the stated setup rather than as a universal 30/360 formula.

Key ideas

• A zero-coupon bond’s present value is its ending payment multiplied by a discount factor.
• The example uses a 30/360 day-count convention to measure time between the specified dates.
• The answer reports an approximate discount factor and present value for the stated rate and redemption amount.
• The document does not explain compounding assumptions or date-adjustment details that may affect the formula.

Tags

# DCF Zero Coupon Bond


# DCF Zero Coupon Bond












Using a 30/360 day count what is the exact formula to discount this single zero coupon bond?

```
DayCount:   30/360
Start Date  6/25/2013
End Date    1/1/2020
Discount Rate   3.50%

Present Value   
Ending Value    50,000,000
```

## Answer by Matt Wolf (score 1)

https://quant.stackexchange.com/a/8524

- DF(t1) = 1/((1+r/360)^360*T)

- Using 30/360 Daycount convention, you get 2346 days to discount over.

- Your discount factor should work out to about 0.7961 and hence your PV of the cash flow should be about 39,803,337.23.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.