At what rate of percentage compound interest does a sum of money becomes 4 times itself in 2 years?

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

Answer

Hint: First, we will let the principal sum of money as ‘P’ and the rate of interest as ‘R’. we will use the conditions given in the question and formula of compound interest to form a different equation. And by solving those equations we will find the rate of interest.

Complete step-by-step solution:
Let the principal sum of money be ‘P’.
Let the rate of interest compounded annually be ‘R’.
Given: the amount becomes 1.44 times the principal amount in the span of 2 years.
So, \[A = 1.44 \times P\]----- (1)
By using compound interest formulas. We get,
$A = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$----- (2)
From equation 1 and 2. We get,
$1.44 \times P = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
$\Rightarrow 1.44 = {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
Squaring on both sides.
$\sqrt {1.44} = \left( {1 + \dfrac{R}{{100}}} \right)$
Value of square root 1.44 is 1.2.
$1.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can also write 1.2 as 1 + 0.2.
$1 + 0.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can write 0.2 as 2/10.
$1 + \dfrac{2}{{10}} = \left( {1 + \dfrac{R}{{100}}} \right)$
$\Rightarrow \dfrac{2}{{10}} = \dfrac{R}{{100}}$
$\Rightarrow 2 = \dfrac{R}{{10}}$
$\Rightarrow R = 2 \times 10$
$\Rightarrow R = 20\% $
So, the rate percent compound interest is $20\%.$

Note: Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

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

Nội dung chính

• At what rate percent compound interest, does a sum of money become 1.44 times of itself in 2 years?
• At what rate percent compound interest, does a sum of money become 1.44 times of itself in 2 years?
• If a certain sum of money becomes 9 times itself in 2 years. Find the rate of compound interest?
• Answer (Detailed Solution Below)
• At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?
• At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years 25% 100% 60% 50%?
• At what rate percent per annum will a sum of money becomes 5 by 4 of itself in 10 years?
• At what rate percent compound interest does a sum of money becomes?
• At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?
• At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years 25% 100% 60% 50%?
• At what rate percent compound interest does a sum of money becomes 9 times in 2 years?
• At what rate percent per annum will a sum of money becomes 5 by 4 of itself in 10 years?

Answer

Hint: First, we will let the principal sum of money as ‘P’ and the rate of interest as ‘R’. we will use the conditions given in the question and formula of compound interest to form a different equation. And by solving those equations we will find the rate of interest.

Complete step-by-step solution:
Let the principal sum of money be ‘P’.
Let the rate of interest compounded annually be ‘R’.
Given: the amount becomes 1.44 times the principal amount in the span of 2 years.
So, \[A = 1.44 \times P\]----- (1)
By using compound interest formulas. We get,
$A = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$----- (2)
From equation 1 and 2. We get,
$1.44 \times P = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
$\Rightarrow 1.44 = {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
Squaring on both sides.
$\sqrt {1.44} = \left( {1 + \dfrac{R}{{100}}} \right)$
Value of square root 1.44 is 1.2.
$1.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can also write 1.2 as 1 + 0.2.
$1 + 0.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can write 0.2 as 2/10.
$1 + \dfrac{2}{{10}} = \left( {1 + \dfrac{R}{{100}}} \right)$
$\Rightarrow \dfrac{2}{{10}} = \dfrac{R}{{100}}$
$\Rightarrow 2 = \dfrac{R}{{10}}$
$\Rightarrow R = 2 \times 10$
$\Rightarrow R = 20\% $
So, the rate percent compound interest is $20\%.$

Note: Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

Let Principal = Rs. y
Then Amount= Rs 1.44y
n= 2 years

Nội dung chính

• At what rate percent compound interest, does a sum of money become 1.44 times of itself in 2 years?
• If a certain sum of money becomes 9 times itself in 2 years. Find the rate of compound interest?
• Answer (Detailed Solution Below)
• At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?
• At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years 25% 100% 60% 50%?
• At what rate percent per annum will a sum of money becomes 5 by 4 of itself in 10 years?
• At what rate percent compound interest does a sum of money becomes?

∴ Amount = `"P"( 1 + "r"/100 )^n`

⇒ 1.44y  = `y( 1 + r/100)^2`

⇒ `[1.44y]/y = ( 1 + r/100)^2`

⇒ `36/25 = ( 1 + r/100)^2`

⇒ `( 6/5 )^2 = ( 1 + r/100)^2`

On comparing,
`6/5 = 1 + r/100`

On solving, we get
 r = 20 % 

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

Answer

Verified

Hint: First, we will let the principal sum of money as ‘P’ and the rate of interest as ‘R’. we will use the conditions given in the question and formula of compound interest to form a different equation. And by solving those equations we will find the rate of interest.

Complete step-by-step solution:
Let the principal sum of money be ‘P’.
Let the rate of interest compounded annually be ‘R’.
Given: the amount becomes 1.44 times the principal amount in the span of 2 years.
So, \[A = 1.44 \times P\]----- (1)
By using compound interest formulas. We get,
$A = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$----- (2)
From equation 1 and 2. We get,
$1.44 \times P = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
$\Rightarrow 1.44 = {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
Squaring on both sides.
$\sqrt {1.44} = \left( {1 + \dfrac{R}{{100}}} \right)$
Value of square root 1.44 is 1.2.
$1.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can also write 1.2 as 1 + 0.2.
$1 + 0.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can write 0.2 as 2/10.
$1 + \dfrac{2}{{10}} = \left( {1 + \dfrac{R}{{100}}} \right)$
$\Rightarrow \dfrac{2}{{10}} = \dfrac{R}{{100}}$
$\Rightarrow 2 = \dfrac{R}{{10}}$
$\Rightarrow R = 2 \times 10$
$\Rightarrow R = 20\% $
So, the rate percent compound interest is $20\%.$

Note: Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

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SBI Clerk Prelims Full Test 1

100 Questions 100 Marks 60 Mins

Last updated on Sep 28, 2022

SBI Clerk 2022 Notification Out for 5486 Vacancies. A total of 5008 regular vacancies and 478 backlog vacancies are announced by SBI. The application window for SBI Clerk (Junior Associates) is open from 7th September to 27th September 2022 with an application fee of Rs 750 for General/EWS/OBC candidates. Graduates between the age of 20 to 28 years of age are eligible to apply. The candidates whose applications will be accepted will have to undergo the SBI Clerk selection process consisting of the Preliminary, Main Exam and language test, if applicable .

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

If a certain sum of money becomes 9 times itself in 2 years. Find the rate of compound interest?

1. 50%
2. 100%
3. 200%
4. 80%

Answer (Detailed Solution Below)

Option 3 : 200%

Free

CT 1: Growth and Development - 1

10 Questions 10 Marks 10 Mins

Given:

The sum becomes 9 times in 2 years.

Formula used:

A = P(1 + r/100)t

Calculation:

Let the principal be ‘P’.

⇒ A = P(1 +  r/100)t

⇒ 9P = P(1 + r/100)2

⇒ 9 = (1 + r/100)2

⇒ √9 = 1 + r/100

⇒ 3 = 1 + r/100

⇒ 300 = 100 + r

⇒ r = 200%

∴ The rate of interest is 200%.

⇒ √1 = √9

⇒ 1 = 3

⇒ 2/1 × 100

⇒ 200% 

∴ The rate of interest is 200%.

Last updated on Sep 22, 2022

The Uttar Pradesh Basic Education Board (UPBEB) has released the UPTET Final Result for the 2021 recruitment cycle. The UPTET exam was conducted on 23rd January 2022. The UPBEB going to release the official notification for the UPTET 2022 too soon on its website. The selection of the candidates depends on the scores obtained by them in the written examination. The candidates who will be qualified for the written test will receive an eligibility certificate that will be valid for a lifetime.

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?

1 Answer. ∴ Required Rate is 82.84% per annum.

At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years 25% 100% 60% 50%?

The rate of interest is 50 % per annum. Here, a sum of money becomes 9/4 of itself in 2 years.

At what rate percent per annum will a sum of money becomes 5 by 4 of itself in 10 years?

The rate of interest per annum is 25%.

At what rate percent compound interest does a sum of money becomes?

A=P(1+r100)n1.44p=p(r100)2√1.44=(r100)1.2=1+r1001.2−1=r1000.2×100=rr=20%

At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?

1 Answer. ∴ Required Rate is 82.84% per annum.

At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years 25% 100% 60% 50%?

The rate of interest is 50 % per annum. Here, a sum of money becomes 9/4 of itself in 2 years.

At what rate percent compound interest does a sum of money becomes 9 times in 2 years?

Detailed Solution The sum becomes 9 times in 2 years. Calculation: Let the principal be 'P'. ∴ The rate of interest is 200%.

At what rate percent per annum will a sum of money becomes 5 by 4 of itself in 10 years?

The rate of interest per annum is 25%.

At what rate a sum of money will become four times of itself in 2 years if the interest compounded half yearly?

At what rate percent compound interest does a sum of money becomes 9 4 times itself in 2 years 25% 100% 60% 50%?

At what rate percent compound interest does a sum of money becomes 9 times in 2 years?

At what rate PAA sum of money will become 4 times?