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 time 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! That is precisely what compound interest does to money. Banks and other financial institutions only use compound interest to calculate the amount. 

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.

Sample Questions

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.

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