Distinguishing Perpetual Annuities from Continuous Compounding

Summary

The document asks what a continuously payable annuity means in a fixed-income context. Its answer describes an annuity as a coupon paid at regular intervals and interprets “continuous” as payments continuing indefinitely. It also shows a finite-series present-value expression for coupon payments and adds an explanation of interest compounding on reinvested payments.

These ideas refer to different features: an annuity can be perpetual because it has no final payment date, while continuous payment or continuous compounding describes how payments or interest accrue over time. The response mixes these concepts and gives no complete formula or worked example, so it is an incomplete guide to valuation. Readers should clarify whether they mean a perpetuity, a continuously paid cash flow, or continuous compounding before choosing a present-value model.

Key ideas

• A perpetuity makes scheduled payments indefinitely.
• Continuous payment and continuous compounding describe different financial concepts.
• The response presents a finite coupon series but does not provide a complete valuation example.
• Clarifying the cash-flow timing and compounding convention is necessary before calculating present value.

Tags

# What does continuously payable annuity mean?


# What does continuously payable annuity mean?












I am preparing for F< exam but I am unable to understand the meaning of continuously payable annuity.

What does it mean? An example would be great.

## Answer by Alex Bădoi (score 0, accepted)

https://quant.stackexchange.com/a/22958

in the context of bonds / fixed income an annuity is a payment which is made at regular time intervals - a cupon. A continuous one is simply being paid for an unlimited amount of time.

```
PV = Cupon/ (1+r)^1 + ...... Cupon/ (1+r)^t
```

just to add to Bob's comment above, a "continuously compounding" annuity is re-invested at the same rate every month on top of your principal value and previous annuity payments - gaining interest on interest. the formula is this:

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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