Compound Interest Formula | How is Compound Interest Calculated

Compound interest formula – Let us know how is compound interest calculated and what is the formula for compound interest with some compound interest examples. Also, we can solve questions based on the rate of compound interest formula. Learn how to calculate compound interest accurately.

Compound Interest Formula with Different Terms

Amount (A) = P × [ 1 + R/100 ]^nT

P= Initial Principal
A= Final Amount
T = Time period
R = Rate of interest
n = Number of times the interest is applied per time period

Compound Interest (CI) = Final Amount (A) – Initial Principal (P)

CI = A – P ⇒ P × [ ( 1 + R/100 )^nT – 1 ]

Understand How is CI calculated with an Example Problem

Question1:  Calculate the amount for Rs. 50000 at 10% per annum for 3 years.

Solution:

From above formula for amount is A=P[1+R/100]^nT

Here P=50000, R= 10%, n=1, T= 3 years
A = 50000[1+10/100]^1×3
⇒ 50000[11/10]^1×3
⇒50000×(11/10)×(11/10)×(11/10)
⇒50×11×11×11
⇒66550
The amount if Rs. 50000 at 10% per annum for 3 years is Rs. 66,550.

Question2: Calculate the compound interest for Rs. 50000 at 10% per annum for 3 years.

Solution:

From above formula for the compound interest is CI= A – P= P × [ (1+R/100)^nT – 1 ]

Here P=50000, R= 10%, n=1, T= 3 years
CI=50000 × [ (1+10/100)^1×3 – 1 ]
⇒50000 × [ (11/10)³ – 1 ]
⇒50000 × [ (1331 – 1000)/1000 ]
⇒50000 × [ 331/1000 ]
⇒50 × 331
⇒16500
The compound interest for Rs 50000 at 10% per annum for 3 years is Rs. 16,500.

Rate of Compound Interest Formula with Example 

Rate of Interest (R) = [(A/P)^1/T – 1 ] % per annum

Question: Calculate the annual rate of interest for principal Rs. 25000 which amount to Rs. 100000 for a period of 2 years.

Solution:

From the above formula for the rate of interest is R = [(A/P)^1/T – 1 ] %

Here Principal (P) = 25000,  Amount (A) = 100000, Time Period (T) = 2 years
R = [(100000/25000)^1/2 – 1 ] %
⇒[(4)^1/2 – 1 ] %
⇒[2 – 1 ] %
⇒3%

The annual rate of interest for principal Rs. 25000 which amount to Rs. 100000 for a period of 2 years is 3%.

Some Compound interest formula Questions and answers

Question 1: If the simple Interest for a principle after 2 years at a rate of 10% is 4000, then calculate the compound interest for the same values?
Solution:
we have the formulas CI = SI × (1 + R/200)

here, SI = 4000
R = 10%
T= 2years
Applying the values in the formula
CI = 4000 × ( 1 + 10/200)
⇒ 4000 × ( 21/20 )
⇒ 4200

Question 2: For a principle of 10000 taken for 2years at a rate of 4% calculate the amount if the interest is due half-yearly.

Solution:

Here the rate of interest is considered as half of the original rate. i, e R/2
The time period is considered as twice the original time period I,e 2T

Now, the resultant formula for amount is A=P[1+(R/2)/100]^2T
 Here,

P = 10000
T= 2
R= 4%
Submitting the values in the equation.
A=10000 × [1+(4/2)/100]^2×2

⇒10000 × [1+2/100]⁴

⇒10000 × [51/50]⁴

⇒10,824

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