Question

Ram borrowed a sum of ₹ 30000 from shyam for 3 years. If the rate of interest is 6%per annum compounded annually, find the interest paid by ram to shyam after 3 years .​

Answer 1

Given data : Ram borrowed a sum of ₹ 30000 from shyam for 3 years. The rate of interest is 6% per annum compounded annually.

To find : Find the interest paid by ram to shyam after 3 years ?

Solution : Here, a/c to given data;

➜ Principal, P = ₹ 30000

➜ Rate of interest, R = 6 %

➜ Time period, T = 3 years

Now, by compound amount, ( A ) formula;

➜ A = P {(1 + (R/100)}^(T)

➜ A = 30000 * {(1 + (6/100)}³

➜ A = 30000 * {(100 + 6)/100}³

➜ A = 30000 * {106/100}³

➜ A = 30000 * 106³/100³

➜ A = 30000 * 1191016/1000000

➜ A = 3 * 1191016/100

➜ A = 3573048/100

➜ A = ₹ 35730.48

Now, by formula of compound interest (CI);

➜ CI = Amount - Principal

➜ CI = 35730.48 - 30000

➜ CI = ₹ 5730.48

Answer : Hence, the interest paid by ram to shyam after 3 years is ₹ 5730.48.

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Answer 2

Given

• Money borrowed/Principal = ₹30000.
• Time = 3 years.
• Rate = 6% p.a.
• Compound - Annually.

To Find

• Interest paid by Ram to Shyam.

Solution

We can solve this sum by using two methods.

Lets solve!

Method 1

By Compound Interest formula.

Principal = ₹30000.

Time = 3 years.

Rate = 6% p.a.

$\bigstar \: \: \boxed{\rm{C.I. = P\bigg(1+ \dfrac{R}{100}\bigg)^n-P}} \\ \\ \\ \\\rm:\implies{C.I.=30000\bigg(1+ \frac{6}{100}\bigg)^3-30000} \\ \\ \\\rm:\implies{C.I. = 30000\bigg(1+ \frac{3}{50}\bigg)^3-30000} \\ \\ \\\rm:\implies{C.I. = 30000\bigg( \frac{53}{50}\bigg)^3-30000} \\ \\ \\\rm:\implies{C.I</p><p> = 30000× \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50}-30000} \\ \\ \\\rm:\implies{C.I. = \frac{6×53×53×53}{5×5}-30000} \\ \\ \\\rm:\implies{C.I. = \frac{893262}{25} - 30000} \\ \\ \\\rm:\implies{C.I. =35730.48 - 30000} \\ \\ \\\rm:\implies{Compound \: Interest = ₹5730.48.}$

Therefore, interest paid by Ram is ₹5730.48.

Method 2

By Simple Interest Method.

Amount for the 1st year

Principal = ₹30000.

Rate = 6% p.a.

Time = 1 year.

I = P × R × T/100

⟹ I = 30000 × 6 × 1/100

⟹ I = ₹1800.

A = P + I

⟹ A = 30000 + 1800

⟹ A = ₹31800.

Note - A of 1st year = P of 2nd year.

Amount for the 2nd year

Principal = ₹31800.

Rate = 6% p.a.

Time = 1 year.

I = P × R × T/100

⟹ I = 31800 × 6 × 1/100

⟹ I = ₹1908.

A = P + I

⟹ A = 31800 + 1908

⟹ A = ₹33708.

Note - A of 2nd year = P of 3rd year.

Amount (Final) for the 3rd year

Principal = ₹33708.

Rate = 6% p.a.

T = Time.

I = P × R × T/100

⟹ I = 33708 × 6 × 1/100

⟹ I = ₹2022.48.

A = P + I

⟹ A = 33708 + 2022.48

⟹ Final Amount = ₹35730.48.

Calculating Compound Interest

C.I. = Final Amount - Original Principal

⟹ C.I. = 35730.48 - 30000

⟹ C.I. = 5730.48.

Therefore, interest paid by Ram is ₹5730.48.

Final Answer

• Interest paid by Ram to Shyam after 3 years is ₹5730.48.

Used Abbreviations

• P = Principal.
• R = Rate.
• T = Time.
• n = Time.
• A = Amount.
• I = Simple Interest.
• C.I. = Compound Interest.

Used Formulas

• C.I. = P(1+ R/100)^n - P.
• I = P × R × T/100.
• A = P + I.
• C.I. = Final Amount - Original Principal.

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