Daily Compound Interest Formula with Examples (2024)

Daily Compound Interest Formula: Compound interest is interest earned on both the principal and interest over a specific time period. The interest that accumulates on a principal over time is equally accounted for as the principal. Furthermore, the following period’s interest calculation is based on the cumulative principal value.

Compound interest is the modern way of calculating interest that is utilized for all financial and economic transactions worldwide. Compound interest is computed on a regular interval, such as annually, semi-annually, quarterly, monthly, or daily. It’s as though reinvesting an investment’s interest income allows the money to grow quickly over time.

What is Daily Compound Interest?

Daily compound interest refers to the method by which interest on a loan or investment is calculated daily and added to the principal amount. This means that each day, interest is calculated not only on the original principal but also on any previously accrued interest. As a result, the interest “compounds” over time, which can significantly increase the growth of the investment or debt.

Daily Compound Interest Formula

The daily compound interest formula calculates interest 365 times in a year. Hence the value of n is 365. According to the explanation, the daily compound interest formula is,

A = P (1 + r / n)^nt

And

Compound interest = A – P

C.P = P (1 + r / n)^nt – P

Here,

P represents the principal amount

r represents the rate of interest

t represents the time in years

n represents the number of times the amount is compounding. When calculate compounds interest on daily basis which means that the amount compounds 365 times in a year. i.e., n = 365.

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Examples on Daily Compound Interest Formula

Question 1: A sum of Rs 5000 is borrowed, and the rate is 5%. What is the daily compound interest for two years?

Solution:

Given: Principal (p) = Rs 5000

Rate of interest (r) = 5%

Time(t) = 2 years

To calculate daily compound interest,

= P (1 + r / n)^nt – P

= 5000 {1 + 5/(100 × 365) }^{365 × 2} – 5000

= 5000 {1 + 5/36500}^{365 x 2} – 5000

= 5000 {(36500 + 5)/36500} ^{365 x 2} – 5000

= 5000 {36505/36500}⁷³⁰ – 5000

= 5000 (1.000136)⁷³⁰ – 5000

= 5000 (1.10436) – 5000

= 5521 .8 – 5000

= 521.80

So the daily compound interest will be Rs 521.80.

Question 2: A person has invested Rs 2000 in a bank where your amount gets compounded daily at an interest rate of 3%. Then what is the amount you get after 5 years? Calculate it by the daily compound interest formula?

Solution:

To find: The amount after 5 years.

The principal amount is, P = Rs 2000.

The rate of interest is, r = 3% = 3/100 = 0.03.

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The time in years is, t = 5 years.

Daily compound interest formula is,

A = P (1 + r / 365)^{365 t}

A = 2000 ( 1+ 0.03/365)^365×5

A = 2000 (365.03/365)¹⁸²⁵

= 2000(1.00008)¹⁸²⁵

= 2000 (1.15718)

= 2314.36

Then the amount person will get after 5 years will be Rs 2314.36.

Question 3: A sum of Rs 10000 is borrowed, and the rate is 2%. What is the daily compound interest for four years?

Solution:

Given: Principal (p) = Rs 10000

Rate of interest (r) = 2 %

Time(t) = 4 years

To calculate daily compound interest,

= P (1 + r / n)^nt – P

= 10000 {1 + 2/(100 × 365)}^{365 x 4} – 10000

= 10000 {1 + 2/36500}^{365 x 4} – 10000

= 10000 {(36500 + 2)/36500} ^{365 x 4} – 10000

= 10000 {36502/36500}¹⁴⁶⁰ – 10000

= 10000 (1.000054)¹⁴⁶⁰ – 10000

= 10000 (1.08202) – 10000

= 10820.20 – 10000

= 820.80

So the daily compound interest will be Rs 820.80.

Question 4: A person has invested Rs 25650 in a bank where the amount gets compounded daily at an interest rate of 6 %. Then what is the amount you get after 6 years? Calculate it by the daily compound interest formula? What will the daily compound interest?

Solution:

To find: The amount after 6 years.

The principal amount is, P = Rs 25650.

The rate of interest is, r = 6% = 6/100 = 0.06.

The time in years is, t = 6 years .

Daily compound interest formula is,

A = P (1 + r / 365)^{365 t}

A = 25650 (1 + 0.06/365)^{365 × 6}

A = 25650 (365.06/365)²¹⁹⁰

= 25650 (1.000164)²¹⁹⁰

= 25650 (1.43208)

= 36732

Then the amount person will get after 5 years will be Rs 36732

And daily compound interest will be = Compound interest = A – P

= 36730 – 25650

= Rs 11080

Question 5: A sum of Rs 5500 is borrowed, and the rate is 2.5%. What is the daily compound interest for 3 years?

Solution:

Given: Principal (p) = Rs 5500

Rate of interest (r) = 2.5 %

Time(t) = 3 years

To calculate daily compound interest,

= P (1 + r / n)^nt – P

= 5500 {1 + 2.5/(100 × 365) }^{365 x 3} – 5500

= 5500 {1 + 25/365000}^{365 x 3} – 5500

= 5500 {(365000 + 25)/365000} ^{365 x 3} – 5500

= 5500 {365025/365000}¹⁰⁹⁵ – 5500

= 5500 (1.0000684)¹⁰⁹⁵ – 5500

= 5500 (1.07777) – 5500

= 5927.73 – 5500

= 427.73

So the daily compound interest will be Rs 427.73

Question 6: A sum of Rs 900 is borrowed, and the rate is 5%. What is the daily compound interest for five years?

Solution:

Given: Principal (p) = Rs 900

Rate of interest (r) = 5 %

Time(t) = 5 years

To calculate daily compound interest,

= P (1 + r / n)^nt – P

= 900 {1 + 5/(100 × 365) }^{365 x 5} – 900

= 900 {1 + 5/36500}^{365 x 5} – 900

= 900 {(36500 + 5)/36500} ^{365 x 5} – 900

= 900 {36505/36500}¹⁸²⁵ – 900

= 900 (1.000136)¹⁸²⁵ – 900

= 900 (1.28169) – 900

= 1153.52 – 900

= 253.52

So the daily compound interest will be Rs 253.52

Practice Problems on Daily Compound Interest Formula

1. Principal: $1,000
Annual Interest Rate: 3%
Time: 2 years
Calculate the future value of the investment with daily compounding.

2. Principal: $5,000
Annual Interest Rate: 4.5%
Time: 5 years
Determine how much money will be in the account at the end of the period with daily compounding.

3. Principal: $500
Annual Interest Rate: 2.5%
Time: 1 year
Find the amount accumulated after 1 year with daily compounding.

4. Principal: $2,500
Annual Interest Rate: 5%
Time: 3 years
Calculate the total amount in the account after 3 years with daily compounding.

FAQs on Daily Compound Interest Formula with Examples

What is daily compound interest?

Daily compound interest is when interest on an investment or loan is calculated and added to the principal daily. This compounding increases the total return because each day’s interest calculation includes the interest from the previous days, leading to exponential growth of your investment.

How is daily compound interest calculated?

Daily compound interest is calculated using the formula: A = P (1 + r / n)^nt, where P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year (365 for daily), and t is the time the money is invested, in years.

What’s the difference between compound interest and simple interest?

The key difference between compound and simple interest is that compound interest earns interest on both the initial principal and the accumulated interest from previous periods, whereas simple interest earns interest only on the principal amount.

How does the compounding frequency affect returns?

The frequency of compounding can significantly impact your returns. More frequent compounding results in higher returns due to the interest being calculated on a continuously updated principal that includes previously earned interest.