> For the complete documentation index, see [llms.txt](https://vikram-bajaj.gitbook.io/introduction-to-corporate-finance-coursera/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://vikram-bajaj.gitbook.io/introduction-to-corporate-finance-coursera/main-2/time-value-of-money/compounding.md).

# Compounding

Compounding is the process of moving CFs forward in time.

The value of a CF at a future point in time is called its **future value**. Future Value $$FV\_t(CF\_i)$$ denotes the future value of $$CF\_i$$ at a future timestamp t.

### Simple Example

```
How much money will we have four years from today if we save $100 a year, beginning today, for the next 
three years, assuming we earn 5% per annum?
```

First, place the CFs on a timeline:

![](/files/-M5-0_eF2GFtBCo5ujzQ)Then, find their future values at timestamp 4, using compounding:

![](/files/-M5-0_eHICEKU2Pt3oTe)Then, aggregate the future values. We get $452.564.

Therefore, the future value four years from today of saving $100 starting today for the next three years at 5% per annum is $452.56.

### Note

We can use a combination of compounding and discounting, allowing us to aggregate CFs at any timestamp.

## ![](/files/-M5-0_eJ0T_H3aMhxlPx)


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