**Daily Compound Interest Formula (Table of Contents)**

- Daily Compound Interest Formula
- Examples of Daily Compound Interest Formula (With Excel Template)
- Daily Compound Interest Formula Calculator

## Daily Compound Interest Formula

Compounding is the effect where an investment earns interest not only on the principal component but also gives interest on interest. So compounding is basically Interest on interest. When we say that the investment will be compounded annually, it means that we will earn interest on the annual interest along with the principal. Daily compounding is basically when our daily interest/return will get the compounding effect. The concept is such that it assumes that the interest earned every day is reinvested at the same rate and will get increased as the time passes. That is the reason that if we annualized the daily compound interest, it will be always higher than the simple interest rate.

Formula For daily compound interest:

Generally, the rate of interest on investment is quoted on per annum basis. So the formula for an ending investment is given by:

**Ending Investment = Start Amount * (1 + Interest Rate) ^ n**

Where n – Number of years of investment

This formula is applicable if the investment is getting compounded annually, means that we are reinvesting the money on an annual basis. For daily compounding, the interest rate will be divided by 365 and n will be multiplied by 365, assuming 365 days in a year.

So

**Ending Investment = Start Amount * (1 + Interest Rate / 365 ) ^ (n * 365)**

**Daily Compound Interest = Ending Investment – Start Amount**

**Daily Compound Interest = [Start Amount * (1 + (Interest Rate / 365)) ^ (n * 365)] – Start Amount**

**Daily Compound Interest = [Start Amount * (1 + Interest Rate) ^ n] – Start Amount**

**Examples of Daily Compound Interest Formula (With Excel Template)**

Let’s take an example to understand the calculation of Daily Compound Interest in a better manner.

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#### Daily Compound Interest Formula – Example #1

**Let say you have $1000 to invest and you can leave that amount for 5 years. Financial institution in which you are depositing the money is offering you 10% interest rate which will be compounded daily. Calculate the Daily Compound Interest.**

**Solution:**

**For Daily Compounding:**

Ending Investment is calculated using the formula given below

**Ending Investment = Start Amount * (1 + Interest Rate / 365 ) ^ (n * 365)**

- Ending Investment = $1,000 * (1 + (10% / 365)) ^ (5 * 365)
- Ending Investment =
**$1,648.61**

Daily Compound Interest is calculated using the formula given below

**Daily Compound Interest = Ending Investment – Start Amount**

- Daily Compound Interest =$1,648.61 – $1,000
- Daily Compound Interest =
**$648.61**

Daily compound interest which you have earned $648.60.

**If the given rate is compounded annually, then**

**For Annual Compounding**

Ending Investment is calculated using the formula given below

**Ending Investment = Start Amount * (1 + Interest Rate) ^ n**

- Ending Investment = $1,000 * (1 + 10%) ^ 5
- Ending Investment =
**$1,610.51**

Daily Compound Interest is calculated using the formula given below

**Daily Compound Interest = Ending Investment – Start Amount**

- Daily Compound Interest =$1,610.51 – $1,000
- Daily Compound Interest =
**$610.51**

So you can see that in daily compounding, the interest earned is more than annual compounding.

#### Daily Compound Interest Formula – Example #2

**Let say you have got a sum of amount $10,000 from a lottery and you want to invest that to earn more income. You do not need that funds for another 20 years. You approached 2 banks which gave you different rates:**

**Bank 1:**Interest Rate: 12.5% Compounding Daily**Bank 2:**Interest Rate: 12.5% Compounding Annually

**Solution:**

**Interest Rate: 12.5% Compounding Daily**

Ending Investment is calculated using the formula given below

**Ending Investment = Start Amount * (1 + Interest Rate / 365 ) ^ (n * 365)**

- Ending Investment = $10,000 * (1 + (12.5% / 365)) ^ (20 * 365)
- Ending Investment =
**$121,772.81**

Daily Compound Interest is calculated using the formula given below

**Daily Compound Interest = Ending Investment – Start Amount**

- Daily Compound Interest = $121,772.81 – $10,000
- Daily Compound Interest =
**$111,772.81**

**Interest Rate: 12.5 % Compounding Annually**

Ending Investment is calculated using the formula given below

**Ending Investment = Start Amount * (1 + Interest Rate) ^ n**

- Ending Investment = $10,000 * (1 + 12.5%) ^ 20
- Ending Investment =
**$105,450.94**

Daily Compound Interest is calculated using the formula given below

**Daily Compound Interest = Ending Investment – Start Amount**

- Daily Compound Interest = $105,450.94 – $10,000
- Daily Compound Interest =
**$95,450.94**

So If we see, effectively, you are earning more if you choose to invest in Bank 1 due to daily compounding.

### Explanation

Compounding is a very intriguing concept in finance but there is some assumption which sometimes does not make much practical sense. Like in daily compounding, it is assumed that all the interest amount will be reinvested at the same rate for the investment period but actually, the interest rate never remains the same and varies. Because of which we might not be able to invest our money at the same rate and our effective return might differ. So basically, this is kind of theoretical representation which tells us that what we might end up with if all the money is reinvested at the end of each day at that rate.

### Relevance and Uses of Daily Compound Interest Formula

Compounding as a whole is helpful in earning interest on interest, which makes logical sense. In simple interest, you earn interest on the same principal for the investment term and you basically lose out income which you can earn on that additional amount. So for example: if you have $100 and the simple interest rate is 10%, for 2 years, you will have 10%*2*100 = $20 as interest. But if you invest that only for 1 year, then you will earn $10 and then again you invest $110 at 10% for a year, you will have $11 interest in 2^{nd} year. So in total, you have $21 interest and you were losing out on $1 interest in case of simple interest. For daily compounding, we can say that, the more the merrier. As you increase the compounding frequency, you will effectively earn more money since your money will go through more rounds of compounding.

### Daily Compound Interest Formula Calculator

You can use the following Daily Compound Interest Calculator

Start Amount | |

Interest Rate | |

n | |

Daily Compound Interest | |

Daily Compound Interest = | [Start Amount * (1 + Interest Rate)^{n}]-Start Amount |

= |
[0 * (1 + 0)^{0}]-0 =
0 |

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