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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