Question

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Topic - Simple and Compound Interest
Class - 8

1. ₹30,000 is invested for some period at 8% p.a. to earn ₹2400 as the simple interest. If the same sum is invested for the same period at the same rate of interest compounded half-yearly, find the compound interest.
Answer = ₹2448
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2. A sum of money is invested for 2 years at the rate of 12% per annum compounded annually. If it was invested at simple interest, the interest would be 72 less than the compound interest. Find the sum of money.
Answer = ₹5000
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Answer 1

Given :-

• Invested sum = ₹30000
• Simple interest = ₹2400
• Rate of interest = 8%

To Find :-

• Compound interest (CI) = ?
• Time given for interest = ?

Solution :-

To calculate the period and compound interest at first we have to find time. Then calculate compound interest. To calculate time we have to use formula of simple interest. Notice in the question in compound interest is given half yearly so, time and rate will be changed. Time = t × 2 and Rate = r/2.

Calculation for Case - (I) :-

[P = 30000. R = 8%. T = ? SI = 2400]

⇢ T = SI × 100/P × R

⇢ T = 2400 × 100/30000 × 8

⇢ T = 24 × 1/3 × 8

⇢ T = 1 years

Calculation for case - (ii) :-

[P = 30000. T = 2 years. R = 4% :-]

⇢ CI = P(1 + r/100)^n - P

⇢ CI = 30000(1 + 4/100)² - 30000

⇢ CI = 30000(104/100)² - 30000

⇢ CI = 30000 × (1.04)² - 30000

⇢ CI = 30000 × 1.0816 - 30000

⇢ CI = 32448 - 30000

⇢ CI = ₹2448

Hence, the required period (t) = 1 years :-

Hence, the compound interest = ₹2448 :-

Question - (2) :-

Given :-

A sum of money is invested for 2 years at the rate of 12% per annum compounded annually. If it was invested at simple interest, the interest would be 72 less than the compound interest.

To Find :-

• The sum of money = ?

Solution :-

To calculate Sum of money at first we have to set up equation as per the given clue in the question. Let the sum of money be P.

Calculation for Case (1) :-

[P = P. R = 12%. T = 2 years :-]

⇢ CI = P(1 + 12/100)² - P

⇢ CI = P(112/100)² - P

⇢ CI = P(1.12)² - P

⇢ CI = P × 1.2544 - P

⇢ CI = 1.2544P - P

⇢ CI = 0.2544P------(i)

Calculation for case (2) :-

[P = P. T = 2. R = 12 %. SI ? ]

⇢SI = P × T × R/100

⇢SI = P × 2 × 12/100

⇢SI = 24P/100

Here SI is less ₹72 then CI

⇢ CI = 24P/100 + 72 ------(ii)

Putting together eq (I) and (II) :-]

⇢ 0.2544P = 24P/100 + 72

⇢ 0.2544P - 24P/100 = 72

⇢ 25.44P - 24P/100 = 72

⇢ 1.44P = 72 × 100

⇢ 1.44P = 7200

⇢ P = ₹5000

Answer 2

1) 30,000 is invested for some period at 8% p.a. to earn ₹2400 as the simple interest. If the same sum is invested for the same period at the same rate of interest compounded half-yearly, find the compound interest.

First let's get the Simple Interest

Let us assume the time be a

• SI = PRT/100

• 2400 = (30000 × 8 × a)/100

• 2400 = 240000a/100

• 2400 = 2400a

• a = 2400/2400

• a = 1

Hence, time is 1 year

Now, getting the compound Interest

➛ A = P(1 + r/200)²ⁿ

➛A = 30000(1 + 8/200)²

➛ A = 30000(1 + 1/25)²

➛ A = 30000 × (26/25)²

➛ A = 30000 × 676/625

➛ A = 48 × 676

★ A = 32448

Henceforth, the amount is 2448

Now, as we know that Compound Interest is Amount - Principal. So,

• CI = A - P

• CI = 32448 - 30000

• CI = 2448

␥ The Compound Interest is ₹2448

2) A sum of money is invested for 2 years at the rate of 12% per annum compounded annually. If it was invested at simple interest, the interest would be 72 less than the compound interest. Find the sum of money.

Using the formula for getting amount

⟹ A = P(1 + r/100)ⁿ

⟹ A = P(1 + 12/100)²

⟹ A = P(1 + 3/25)²

⟹ A = P(28/25)²

⟹ A = P × 784/625

⟹ A = 784/625P

Now, we need to subtract the principal from the amount

So, let be be the Principal

⟹ A = 784/625P - P

⟹ A = (784P - 625P)/625

★ A = 159/625P

Now, according to the formula of Simple Interest we get

☞ SI = (P × R × T)/100

☞ SI = P × 12 × 2/100

☞ SI = 24/100P

★ SI = 6/25P

Now, subtracting SI from the amount we get which is 72 less than the interest

➻ Amount - SI = 72

➻ 159/625P - 6/25P = 72

➻ 159/625P - 150/625P = 72

➻ 9/625P = 72

➻ P = 72 × 625/9

➻ P = 8 × 625

★ P = 5000

␥ Henceforth, the sum of money is ₹5000