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 Semi-Annually 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 half-yearly?

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.