At what rate percent compound interest does a sum of money become 1.21 times of itself in 2 years?

Correct Answer:

Description for Correct answer:
Let the principal = Rs. P

Time = 2 years

Amount = Rs.2.25 P

Let Rate % = R %

By using formula,

2.25P=\( \Large P \left(1+\frac{R}{100}\right)^{2}\)

\( \Large \frac{225}{100}= \left(1+\frac{R}{100}\right)^{2}\)

\( \Large\left(\frac{15}{10}\right)^{2}= \left(1+\frac{R}{100}\right)^{2} \)

\( \Large \frac{R}{100}=\frac{15}{10}-1 \)

=\( \Large \frac{R}{100}=\frac{5}{10} \)

R = 50 %

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Given:

A sum becomes 1.44 times of itself.

Time = 2 years

Formula used:

A = P(1 + R/100)T

Where,

A = Amount, P = Sum or Principal

R = Rate of interest

T = Time

Calculation:

Let the Principal be 100

Then Amount becomes 144

Now, A = P(1 + R/100)T

⇒ 144 = 100 × (1 + R/100)2

⇒ (144/100) = (1 + R/100)2

⇒ (12/10)2 = (1 + R/100)2

Now, 12/10 = 1 + (R/100)

⇒ 2/10 = R/100

⇒ R = 20%

∴ The rate of interest is 20%.

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

A certain principal invested at compound interest becomes 1.21 times of itself in 2 years. If thrice this principal were lent at simple interest at the same rate, in how many years would it double itself?

1. 5 years
2. 10 years
3. 15 years
4. 20 years

Answer (Detailed Solution Below)

Option 2 : 10 years

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GIVEN:

A = 1.21P, time = 2 years

CONCEPT:

Simple and Compound interest concept.

FORMULA USED:

SI = PRT/100

For CI:

A = P(1 + R/100)T

Where P is principal, R is rate of interest and T is time.

CALCULATION:

According to the question:

1.21P = P(1 + R/100)2

⇒ (1 + R/100)2 = 1.21

⇒ (1 + R/100) = 1.1

⇒ R = 10

So, rate of interest = 10%

Now,

Principal = 3P and Amount = 6P

So,

SI = 6P – 3P = 3P

So,

3P = (3P × 10 × T)/100

⇒ T = 10

Hence, required time = 10 years

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

∴ 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 % 

Q.

A sum of Rs. 44,200 is divided between John and Smith, 12 years and 14 years old respectively, in such a way that if their portions be invested at 10 percent per annum compound interest, they will receive equal amounts on reaching 16 years of age.

(i) What is the share of each out of Rs. 44,200 ?

(ii) What will each receive, when 16 years old ?

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

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At what rate percent compound interest does a sum of money double itself in 12 years?