At what rate percent per annum will 6000 amount to 6615 in 2 years compounded annually?

What is the amount of Rs.6,000 at the rate of 5% per annum for 2 years, when interest is compounded annually?

1. Rs. 6615
2. Rs. 6655
3. Rs. 6775
4. Rs. 6900

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• What is the amount of Rs.6,000 at the rate of 5% per annum for 2 years, when interest is compounded annually?
• Answer (Detailed Solution Below)
• At what rate per cent per annum will $Rs\,6000$ amount to $Rs\,6615$ in two years when interest is compounded annually?
• At what rate per cent compound interest does a sum of money become 1.44 times of itself in 2 years?
• At what rate of interest per annum ₹ 600 will become ₹ 661.50 in 2 years the interest being compounded annually?
• What sum will become rupees 6000 after 2 years at 5% per annum when the interest is compounded annually?
• In what time will rupees 6000 amount to rupees 6000 615 at 5 per annum compounded annually?

Answer (Detailed Solution Below)

Option 1 : Rs. 6615

Free

CT 1: Growth and Development - 1

10 Questions 10 Marks 10 Mins

Given:

Principal of Rs.6000 at 5% p.a. for 2 years

Formula used:

Amount = Principal × (1 + r/100)n

Calculation:

Amount = 6000 × (1 + 5/100)2

⇒ 6000 × 21/20 × 21/20 = 6615

∴ Amount = Rs.6615

Alternate Method Effective rate of interest for 2 years = r + r + (r × r)/100

⇒ 5 + 5 + (5 × 5)/100 = 10 + 0.25 = 10.25%

Amount is calculated on Principal that is100% of itself.

So, Amount = Principal + Interest = 100% + 10.25% = 110.25%

∴ Amount = Rs.6000 × 110.25% = Rs.6615

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At what rate per cent per annum will $Rs\,6000$ amount to $Rs\,6615$ in two years when interest is compounded annually?

Answer

Verified

Hint: The problem can be solved easily with the concept of compound interest. Compound interest is the interest calculated on the principal and the interest of the previous period. The amount in compound interest to be cumulated depends on the initial principal amount, rate of interest and number of time periods elapsed. The amount A after a certain number of time periods T on a given principal amount P at a specified rate R compounded annually is calculated by the formula: $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$ .

Complete step-by-step answer:
In the given problem,
Principal $ = P = Rs\,6,000$
Rate of interest $ = R\% $
Time Duration $ = 2\,years$
In the question, the period after which the compound interest is compounded or evaluated is given as a year.
So, Number of time periods $ = n = 2$
Now, The amount A to be paid after a certain number of time periods n on a given principal amount P at a specified rate R compounded annually is calculated by the formula: $A = P{(1 + \dfrac{R}{{100}})^T}$ .
Hence, Amount $ = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
Substituting the values of known quantities, we get,
$ \Rightarrow 6615 = 6000{\left( {1 + \dfrac{R}{{100}}} \right)^2}$
Shifting the terms in the equation, we get,
$ \Rightarrow {\left( {1 + \dfrac{R}{{100}}} \right)^2} = \dfrac{{6615}}{{6000}}$
Cancelling common factors in numerator and denominator, we get,
 $ \Rightarrow {\left( {1 + \dfrac{R}{{100}}} \right)^2} = \dfrac{{441}}{{400}}$
Taking square root on both sides of equation, we get,
$ \Rightarrow \left( {1 + \dfrac{R}{{100}}} \right) = \sqrt {\dfrac{{441}}{{400}}} $
We know that square roots of $441$ and $400$ are $21$ and $20$ respectively. So, we get,
$ \Rightarrow \left( {1 + \dfrac{R}{{100}}} \right) = \dfrac{{21}}{{20}}$
Isolating the variable R. we get,
$ \Rightarrow \dfrac{R}{{100}} = \dfrac{{21}}{{20}} - 1$
Taking LCM of fractions,
$ \Rightarrow \dfrac{R}{{100}} = \dfrac{{21 - 20}}{{20}}$
Multiplying both sides of equation by $100$,
$ \Rightarrow R = \dfrac{1}{{20}} \times 100$
Simplifying the calculations, we get,
$ \Rightarrow R = 5$
So, the rate of interest per annum for which $Rs\,6000$ amounts to $Rs\,6615$ in two years is $5\% $.
So, the correct answer is “ $5\% $”.

Note: Time duration is not always equal to the number of time periods. The equality holds only when the compound interest is compounded annually. If the compound interest is compounded half yearly, then the number of time periods doubles in the given time duration and the rate of interest in each time period becomes half of the specified rate of interest. Care should be taken while doing calculations.

At what rate per cent compound interest does a sum of money become 1.44 times of itself in 2 years?

Detailed Solution A sum becomes 1.44 times of itself. ∴ The rate of interest is 20%.

At what rate of interest per annum ₹ 600 will become ₹ 661.50 in 2 years the interest being compounded annually?

R=5% Was this answer helpful?

What sum will become rupees 6000 after 2 years at 5% per annum when the interest is compounded annually?

∴ Amount = Rs.6000 × 110.25% = Rs.6615 The UPTET exam was conducted on 23rd January 2022.

In what time will rupees 6000 amount to rupees 6000 615 at 5 per annum compounded annually?

At 5% per annum the sum of Rs. 6,000 amounts to Rs. 6,615 in 2 years when the interest is compounded annually.

What sum will become rupees 6000 after 2 years at 5% per annum when the interest is compounded annually?

At what rate of interest per annum ₹ 600 will become ₹ 661.50 in 2 years the interest being compounded annually?

In what time will rupees 6000 amount to rupees 6000 615 at 5 per annum compounded annually?

At what rate percentage per annum will a sum of Rs 5000 amount to Rs 6000 in 4 years?