Daily Compound Interest Formula with Examples

Compound interest is interest earned on both the principal and interest over a specific 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.

It 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)
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 numbr 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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Solve Examples on Daily Compound Interest Formula

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

Given:
Principal (p) = ₹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 ₹521.80.

Question 2: A person has invested ₹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 = ₹2000.
The rate of interest is, r = 3% = 3/100 = 0.03.
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 ₹2314.36.

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

Given:
Principal (p) = ₹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 ₹820.80.

Question 4: A person has invested ₹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 = ₹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 ₹36732 

And daily compound interest will be = Compound interest =  A - P 
= 36730 - 25650
=  ₹11080

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

Given: Principal (p) = ₹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 ₹427.73

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

Given: Principal (p) = ₹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 ₹253.52