Question

How long will it take for ₹ 5660 invested at 10% p.a. simple interest to amount to ₹ 7641?
step-by-step explanation​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A sum of ₹ 5660 invested at 10% p.a. simple interest to amount to ₹ 7641.

So, it means we have,

Rate of interest, r = 10 % per annum

Principal, P = ₹ 5660

Amount, A = ₹ 7641

So,

Simple Interest, SI = Amount - Principal

Simple interest = 7641 - 5660 = ₹ 1981

Let time period be n years.

We know,

Simple interest (SI) received on a certain sum of money of ₹ P invested at the rate of r % per annum for n years is given by

$\boxed{\rm{  \:SI \: = \: \frac{P \times r \times n}{100} \: \: }}$

So, on substituting the values, we get

$\rm \: 1981 = \dfrac{5660 \times 10 \times n}{100}$

$\rm \: 1981 = 566n$

$\rm\implies \:n \: = \: 3.5 \: years$

So, ₹ 5660 invested at 10% p.a. simple interest to amount to ₹ 7641 in 3.5 years.

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

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{P = \dfrac{SI \times 100}{r \times n} }\\ \\ \bigstar \: \bf{r = \dfrac{SI \times 100}{P \times n} }\\ \\ \bigstar \: \bf{n = \dfrac{SI \times 100}{P \times r} }\\ \\ \bigstar \: \bf{Amount = P\bigg(\dfrac{100 + rn}{100} \bigg) }\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

Given :-

• A sum of Rs 5660 invested at 10% per annum simple interest to amount to Rs 7641 .

To Find :-

• What is the time period.

Solution :-

First, we have to find the simple interest :

As we know that :

$\clubsuit$ Simple Interest Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Simple\: Interest =\: A - P}}}\: \: \: \bigstar$

where,

• A = Amount
• P = Principal

Given :

• Amount = Rs 7641
• Principal = Rs 5660

According to the question by using the formula we get,

$\implies \sf Simple\: Interest =\: Rs\: 7641 - Rs\: 5660$

$\implies \sf\bold{\red{Simple\: Interest =\: Rs\: 1981}}$

Hence, the simple interest is Rs 1981 .

Now, we have to find the time period :

As we know that :

$\clubsuit$ Time Period Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{T =\: \dfrac{S.I \times 100}{P \times r}}}}\: \: \: \bigstar$

where,

• T = Time Period
• S.I = Simple Interest
• P = Principal
• r = Rate of Interest

Given :

• Simple Interest = Rs 1981
• Principal = Rs 5660
• Rate of Interest = 10%

According to the question by using the formula we get,

$\implies \sf T =\: \dfrac{1981 \times 100}{5660 \times 10}$

$\implies \sf T =\: \dfrac{1981\cancel{00}}{566\cancel{00}}$

$\implies \sf T =\: \dfrac{1981}{566}$

$\implies \sf\bold{\red{T =\: 3.5\: years}}$

$\therefore$ The time period is 3.5 years .

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