Question

4. I borrowed ₹ 12000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?
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Answer 1

Given :

• Principle borrowed = ₹12000
• Rate of interest = 6%
• Time of interest = 2 years

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To Find :

The extra mony paid by you if you had borrowed sum for compound interest with same rate .

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Formula To Be applied :

We will use the formula of simple Interest and Compound interest:

• SI = PTR/100
• CI + P = P(1 + R/T)^T

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Process:

Here I will tell you two methods of finding extra interest of Compound Interest :

Method 1 :

• We will first find the SI of the Principle
• Then, for compound interest we will calculate SI for first year
• Find the amount for first year.
• Then, we will find the SI for second year with the amount of first year.
• Thus we can get the CI if the Principle.
• Now, we can subtract the SI with CI to get the extra interest.

Method:

• we will find the SI with normal Method,
• Ci with normal Method,
• Subtract SI from CI to find Extra interest.

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Solution :

Method 1 :

Given, Principle= 12000

Time = 2 years

Rate = 6%

Hence, SI = PTR/100

SI = (12000×2×6)/100

SI = 120×2×6

Hence, SI = ₹1440

Hence, Simple Interest for two years = 1440

Now, we will calculate the CI with the help of First Method.

So, SI for First year = PTR/100

SI = 12000×1×6/100

SI = 120×6

Hence, SI for first year = 720

Now, the amount for first year = 12720,

Now, we will calculate the SI on the amount for second year.

SI = PTR/100

SI = 12720×1×6/100

SI = 127.2×6

Hence, SI for second year = 763.2 years.

So, CI on amount = 720+763.2

Or, CI = ₹1483.2

Hence, extra Amount = CI-SI

or, extra amount = 1483.2-1440

or, extra amount = 43.2

Hence, extra Interest = ₹43.2

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Method 2 :

As we have already calculated SI In previous Method,

SI = 1440

Now, we will calculate the CI with normal Method.

CI+P = P(1+ R/100)^T

or, CI+P = 12000(1+ 6/100)²

or, CI+12000 = 12000(106/100)²

or, CI + 12000 = 12000× 11236/10000

Or, CI + 12000 = 1.2×11236

Or, CI = 13483.2-12000

Hence, CI = 1483.2

Hence, extra Interest = 1483.2-1440

or, extra interest = 43.2 rupees.

Choose the method you liked most ! .

Answer 2

▩ Solution :-

➸ Simple Interest

• Principal (P) = ₹12000

• Rate (R) = 6% p.a.

• Time (T) = 2 years

Now, finding interest,

$\tt Interest (I) = \dfrac{P \times R \times T}{100}$

$\tt Interest (I) = \dfrac{120\cancel{00} \times 6 \times 2}{1\cancel{00}}$

$\tt Interest (I) = \dfrac{120 \times 12}{1}$

$\tt Interest (I) = 1440$

Now, Amount (A) = Principal + Interest

A = 12000 + 1400

$\sf \fbox{A = 13400}$

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➸ Compound Interest

• Principal (P) = ₹12000

• Rate (R) = 6% p.a.

• Time (T) = 2 years

$\tt Amount (A) = P{(1 + \frac{R}{100})}^{t}$

$\tt Amount (A) = 12000{(1 + \frac{6}{100})}^{2}$

$\tt Amount (A) = 12000{(\frac{100 + 6}{100})}^{2}$

$\tt Amount (A) = 12000{(\frac{106}{100})}^{2}$

$\tt Amount (A) = 12000(\frac{106}{100} \times \frac{106}{100})$

$\tt Amount (A) = 12000(\frac{11236}{10000})$

$\tt Amount (A) = 12\cancel{000}(\frac{11236}{10\cancel{000}})$

$\tt Amount (A) = 12 \times (\frac{11236}{10})$

$\tt Amount (A) = \frac{134832}{10}$

$\tt \fbox{Amount (A) = 13483.2}$

∴ Amount using Simple Interest = ₹13440

& Amount using Compound Interest = ₹13483.2

➸ Extra Amount = Amount Using Compound Interest - Amount Using Simple Interest

Extra Amount = 13483.2 - 13400

$\sf →\fbox \green{Extra \: Amount = 43.2}$

∴ I have to pay ₹43.3 extra.