Compound Interest Definition
Compound interest is calculated by adding the principal and existing interest over a particular period. The interest earned on principal over time is added to the principal and becomes the new principal amount for the following time period. Again, the interest for the next period is calculated using the entire principal value. Compound interest is normally denoted by C.I.
$$ Compound\ Interest\ Formula\ CI = P(1+\frac{r}{n})^{nt} p. $$
Where,
A = amount
P = principal
r = rate of interest
n = number of times interest is compounded per year
t = time (in years)
Alternatively, we can write the formula as given below: C.I = A – P
The formula for calculating total compounded amount is as follows:
$$ A=P(1+\frac{r}{n})^{nt} $$
For an initial principal of P, rate of interest per annum of r%, time period t in years, frequency of compounding the interest annually n,
Interest compounded across different years
Let us look at the values of Amount in the case of compound interest for different years.
Time  Formula 
Compounded Annually Formula  $$ A = P (1 + r)^t $$ 
Compounded SemiAnnually Formula  $$ A = P (1 + \frac{r}{2})^{2t}$$ 
Compounded Quarterly Formula  $$ A = P (1 + \frac{r}{4})^{4t} $$ 
Compounded Monthly Formula  $$ A = P (1 + \frac{r}{12})^{12t} $$ 
Compounded Weekly Formula  $$A = P (1 + \frac{r}{52})^{52t}$$ 
Compounded Daily Formula  $$A = P (1 + \frac{r}{365})^{365t}$$ 
Practice Quizzes
Compound Interest Quiz 1 – Coming Soon 
Compound Interest Quiz 2 – Coming Soon  Compound Interest Quiz 3 – Coming Soon 
Example problems
Q1. Akash invests Rs. x in insurance which gives her returns at 21% annually and Rs. y in mutual funds which gives her returns of 10% compounded half yearly. If Akash gets the same returns from both the investments after 1 year, then what is the square root of the ratio of x to y?
A) 1:2
B) 11:21
C) 21:22
D) 21:25
E) None of these
Answer: c
Explanation:
Q2. The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is
A) 2 years
B) 2.5 years
C) 3 years
D) 4 years
Answer: A
Explanation:
Amount = Rs.(30000+4347) = Rs.34347
let the time be n years
Then,30000(1+7/100)^{n} = 34347
(107/100)^{n} = 34347/30000 = 11449/10000 = (107/100)^{2}
n = 2years
Q3. What is be the compound interest (in Rs.) accrued on an amount of Rs. 15000 at the rate of 20 per cent annum in two years, if the interest is compounded halfyearly?
Correct Option: D
Explanation:
Rate of interest (half yearly) = 20/2 = 10%
Now, P = 15000, T = 2 = 4 half years
By the net% effect we would calculate the effective compound rate of interest for 4 half years = 46.41% (Refer to subdetails)
Therefore, CI = 46.41% of 15000
$$CI = \frac{46.41 × 15000}{100} = ₹ 6961.5 $$
B) 4 yr.
C) 5 yr.
D) 8 yr.
E) None of theseCorrect Option: A
Explanation:
Q5. Find the compound interest on Rs. 16,000 at 20% per annum for 9 months, compounded quarterly?
A) 2422
B) 2522
C) 2622
D) 2722
Answer: B
Explanation:
Principal = Rs. 16000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522.
CI. = Rs. (18522 – 16000) = Rs. 2522
Q6.What is the difference between the compound interests on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and halfyearly?
A) 2.04
B) 3.04
C) 4.04
D) 5.04
Answer: A
Explanation:
C.I. when interest
compounded yearly= Rs.[5000*(1+4/100)(1+1/2*4/100)] = Rs. 5304.
C.I. when interest is compounded halfyearly=Rs.5000(1+2/100)^{3}= Rs. 5306.04
Difference = Rs. (5306.04 – 5304) = Rs. 2.04
Q7. Find compound interest on Rs. 7000 at 21% per annum for 2 years 4 months, compounded annually.
A) Rs. 3824.9
B) Rs. 3966.1
C) Rs. 4094.4
D) Rs. 11109
Correct Option: B
Explanation:
Q8. If Rs. 1000 amounts to Rs. 1166.40 in two years compounded annually, Find the rate of interest per annum.
A) 2% p.a
B) 4% p.a
C) 6% p.a
D) 8% p.a
Correct Option: D
Explanation:
Latest Job Notifications  Daily Job updates
You Can visit our YouTube channel for the Latest Job Notifications and Online Classes In English: Click Here & For Telugu channel: Click Here


Frequently Asked Questions About Compound Interest
Q1: What is compound interest?
Compound interest is the interest calculated on both the principal and the interest collected over the preceding period.
Q2: How do you calculate compound interest?
Compound interest is calculated by multiplying the initial principal amount (P) by one and the annual interest rate (R) by the number of compound periods (nt) minus one. That is, CI equals P[(1 + R)^nt – 1].
Here, P represents the initial amount.
R = annual interest rate expressed as a percentage.
n = number of compounding periods in a particular time.
Q3: Who gains from compound interest.
Investors gain from compound interest since the interest is calculated based on the principle plus the interest earned before.
Q4: What is the interest compounded quarterly formula?
The formula for interest compounded quarterly is as follows:
$$ A = P (1 + \frac{r}{4})^{4t} $$
Q5: How do you determine the compound interest rate?
The compound interest rate can be calculated using the formula $$ A=P(1+\frac{r}{n})^{nt} $$
A = total amount.
P = Principal, r = Annual nominal interest rate in decimal, and n = Number of compounding periods.
t equals time (in years).
Thus, compound interest (CI) equals A minus P.