Compounding a Series of Daily Rates into a Final Balance

Summary

The document shows how to calculate a final balance when each day has a different rate and interest compounds discretely. Starting from an initial principal, multiply the balance successively by one plus each day’s rate. The same calculation can be expressed as the initial amount multiplied by the product of all daily growth factors, avoiding a separate day-by-day balance calculation. Rates must be represented consistently as decimal proportions for the product to give the intended result.

The answer cautions that this approach is appropriate for discrete compounding, and warns against applying it to rates other than overnight rates without checking the rate convention. It does not explain day-count rules, whether rates are annualized, or how missing days and business-day accrual should be handled. Those details matter in a real financial application, so the product formula alone is not a complete specification of an interest calculation.

Key ideas

• For discrete daily compounding, multiply the principal by one plus each day’s rate.
• The final balance is the product of all daily growth factors times the initial amount.
• The rates must use a consistent decimal representation and compounding convention.
• The answer cautions against applying the method to non-overnight rates without checking their conventions.

Tags

# How to calculate daily interest at different rates each day?


# How to calculate daily interest at different rates each day?












I have the following issue:

I need to calculate the daily income of a financial application over a period based on a percentage of a daily financial index. The problem is that for each day, this index has a different value. For example:

```
Date     value
Apr-1    0,048089%
Apr-2    0,045442%
Apr-3    0,041886%
and so on...
Apr-31   0,035450%
```

On April 1, the initial value of the investment was $ 1,000. How much will the total be on April 31st?

Is there a way to get the final value using a single formula?

The way I do today, I need to calculate the day-to-day balance.

## Answer by vanguard2k (score 0, accepted)

https://quant.stackexchange.com/a/34828

if the values are calculated using discrete compounding, you could do the following.

Formula in Excel:

> =PROD(1+A1:A31)*1000

one line in R

> prod(1+df$value)*1000

A word of warning: if you are using this to compound interest rates other than overnight rates, you are on the wrong track.

Anyway, I will vote to close the question since its too basic.

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