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.
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
Daily Compound Interest Formula with Examples
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.
Table of Content
- What is Daily Compound Interest?
- Daily Compound Interest Formula
- Examples on Daily Compound Interest Formula
- Practice Problems on Daily Compound Interest Formula
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