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Learn how to calculate simple and compound interest with the help of suitable examples.

#### Calculation of **Simple Interest****: **

Simple interest is the interest calculated on the original principal only for the time during which the money lent is being used. Simple interest is paid or earned on the principal amount lent or borrowed.

**Simple interest is ascertained with the help of the following formula: **

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Interest = Pnr

Amount = P (1 + nr)

Where, P = Principal

r = Rate of Interest per annum (‘r’ being in decimal)

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n = Number of years

**Problem 1: **

What is the simple interest and amount of Rs. 8,000 for 4 years at 12% p.a.

**Solution:**

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Interest = Pnr = 8,000 x 4 x 0.12 = Rs. 3,840

Amount (i.e. principal + Interest) = P (1 + nr) = 8,000 [1 + (4 x 0.12)] = 8,000 (1 + 0.48) = Rs. 11,840

Interest = Amount – Principal = 11,840 – 8,000 = Rs. 3,840

**Problem 2: **

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At what rate per cent will Rs.26,435 amount to Rs.31,722 in 4 years?

**Solution:**

A = P(1 + nr)

1,057.40 r = 31,722 – 26,435

r = 5,287/1,057.40 = 5

∴ Rate of interest = 5%

#### Calculation of **Compound Interest****: **

If interest for one period is added to the principal to get the principal for the next period, it is called **“compounded interest”.** The time period for compounding the interest may be annual, semiannual or any other regular period of time. The period after which interest becomes due is called ‘interest period’ or ‘conversion period’. If conversion period is not mentioned, interest is to be compounded annually.

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The formula used for compounding of interest income over ‘n’ number of years.

A = P (1 + i)^{n}

^{}Where, A = Amount at the end of ‘n’ period

P = Principal amount at the beginning of the ‘n’ period

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i = Rate of interest per payment period (in decimal)

n = Number of payment periods

**When interest is payable half-yearly: **

**When interest is payable monthly: **

**When interest is payable quarterly: **

**When interest is payable daily: **

**Problem 3: **

Find out compounded interest on Rs.6,000 for 3 years at 9% compounded annually.

**Solution:**

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A = P (1 + i)^{n} = 6,000(1 +0.09)^{3}= 6,000 (1.09)^{3} = 6,000 x 1.29503 = Rs.7,770

**Problem 4: **

What sum will amount to Rs. 5,000 in 6 years’ time at 8%% per annum.

**Solution:**

A = P (1 + i)n = 5,000 (1 + 0.085)^{6} = 5,000 (1.085)^{6}= 5,000 x 1.63147 = Rs.8,157

**Problem 5: **

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Calculate the compound interest on Rs.800 for 5 years at 12% compounded annually.

**Solution:**

A = P (1 + i)^{n} = 8,000 (1 + 0.12)^{5} = 8,000 x 1.12^{s} = 8,000 x 1.76234 = Rs.14,098.72 say Rs.14,100

Compound interest = Rs.14,100 – Rs.8,000 = Rs.6,100