Question

A sum Rs 800 amount to Rs 960 in 4 years. What will it amount if the rate of interest is increased by  3%?​

Answer 1

★ Concept

Here the above question is based on the concept of Simple Interest. We're provided with Principle as ₹ 800, Amount as ₹ 960 and so does the time period i.e 4 yrs. First of all, we'll calculate Simple Interest and then with the help of that we will find rate of Interest (or initial rate). It's mentioned in the question that the rate of Interest is increased by 3% so we'll add initial rate with increased rate and will get new rate of Interest. This time we will make use of rate of Interest to find first new Simple Interest and then increased amount.

Let's proceed with Calculation !!

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Given that,

↝ Principle = ₹ 800

↝ Amount = ₹ 960

↝ Time Period = 4 years

We Know that,

$\sf \: Simple \: Interest (S.I.) = Amount - Principle$

$\sf » Simple \: Interest = ₹ (960 - 800)$

$\sf \: » Simple \: Interest (Initial) = \red{₹ 160}$

Also, we know that the formula of Simple Interest.

$\underline{\boxed { \sf \: Simple \: Interest = P*R*T/ 100 }}$

Therefore,

$\sf \: R = S.I*100/ P*T$

$\sf \:⇒ R = \dfrac{100 \times 160}{800 \times 4} = \red{5\%}$

Thus, we get initial rate of Interest = 5%

According to question

Rate of Interest is increased by 3%

$\sf New \: Rate \: of \: Interest = Initial \: Interest + Increased \: rate$

New Rate of Interest = (5+3)% = 8%

If rate of Interest increases then its corresponding Simple Interest and Amount will also increases.

$\sf \: ⇒ \: Simple \: Interest = \dfrac{800 \times 8 \times 4}{100} = \red{ ₹ \: 256}$

Now,

New Amount = Simple Interest + Principle

$\sf ⇒ \: New \: Amount = 256 + 800 = \red{₹ \: 1056}$

⇒ Required Amount = ₹ 1056

$\underline{\rule{190pt}{2pt}}$

☞ Additional Information

Here, we deals with increased rate of Interest and with the help of which finds Increased Amount. We know that

Simple Interest = P*R*T/ 100

This means,

• R ∝ S.I.
• P ∝ S.I.
• T ∝ S.I.

Thus any change in rate of Interest, principle or even in Time period causes a change in Simple Interest and since,

Amount = Simple Interest + Principle

Therefore, Amount will also alter.

Answer 2

Step-by-step explanation:

$\rule{190pt}{1pt}$

Given that,

↝ Principle = ₹ 800

↝ Amount = ₹ 960

↝ Time Period = 4 years

We Know that,

$\sf \: Simple \: Interest (S.I.) = Amount - PrincipleSimpleInterest(S.I.)=Amount−Principle</p><p>$

$\sf » Simple \: Interest = ₹ (960 - 800)»SimpleInterest=₹(960−800)$

$\sf \: » Simple \: Interest (Initial) = \red{₹ 160}»SimpleInterest(Initial)=₹160$

Also, we know that the formula of Simple Interest.

$\underline{\boxed { \sf \: Simple \: Interest = P*R*T/ 100 }} </p><p>SimpleInterest=P∗R∗T/100</p><p>$

Therefore,

$\sf \: R = S.I*100/ P*TR=S.I∗100/P∗T$

$\sf \:⇒ R = \dfrac{100 \times 160}{800 \times 4} = \red{5\%}⇒R= </p><p>800×4</p><p>100×160</p><p> </p><p> =5%$

Thus, we get initial rate of Interest = 5%

According to question

Rate of Interest is increased by 3%

$\sf New \: Rate \: of \: Interest = Initial \: Interest + Increased \: rateNewRateofInterest=InitialInterest+Increasedrate$

New Rate of Interest = (5+3)% = 8%

If rate of Interest increases then its corresponding Simple Interest and Amount will also increases.

$\sf \: ⇒ \: Simple \: Interest = \dfrac{800 \times 8 \times 4}{100} = \red{ ₹ \: 256}⇒SimpleInterest= </p><p>100</p><p>800×8×4</p><p> </p><p> =₹256$

Now,

$</p><p>\sf ⇒ \: New \: Amount = 256 + 800 = \red{₹ \: 1056}⇒NewAmount=256+800=₹1056</p><p></p><p>⇒ Required Amount = ₹ 1056</p><p>\underline {\rule{190pt}{2pt}}$

New Amount = Simple Interest + Principle