Question

A certain amount was deposited into a bank account having an interest rate of 5%
If the total amount after 4 years was 1,500, how much was the amount deposited
initially? For the same initial amount, how should the interest rate increase such
that the simple interest would amount to 400?​

Answer 1

Given:

The rate of interest, R = 5%

Time period, T = 4 years

The total amount after 4 years = Rs. 1500

To find:

(i) How much was the amount deposited  initially?

(ii) For the same initial amount, how should the interest rate increase such

that the simple interest would amount to 400?​

Solution:

We have the formulas as:

$\boxed{\bold{S.I. = \frac{PRT}{100} }}\\\\\boxed{\bold{Amount = P + S.I.}}$

(i) Finding the amount deposited initially:

Let "P" represent the initial sum of money.

Using the above two formulas, we can write as:

$A - P = \frac{PRT}{100}$

$\implies 1500 - P = \frac{P\times 5\times 4}{100}$

$\implies 150000 - 100P = P\times 5\times 4$

$\implies 150000 - 100P = 20P$

$\implies 100P + 20P = 150000$

$\implies 120P = 150000$

$\implies P = \frac{150000}{120}$

$\implies \bold{P = Rs.\:1250}$

Thus, the amount deposited initially is Rs. 1250.

(ii) Finding the increase in the rate of interest:

Let the rate of interest is increased by "x" %.

Here

The Simple interest = Rs. 400

The rate of interest = (x + 5)%

Therefore, by using the formula of simple interest, we get

$400 = \frac{1250\times (x+5)\times4}{100}$

$\implies 100 = \frac{1250\times (x+5)}{100}$

$\implies 10000 = 1250\times (x+5)$

$\implies 10000 = 1250x \:+\:6250$

$\implies 10000 - 6250 = 1250x$

$\implies 3750 = 1250x$

$\implies x = \frac{3750}{1250}$

$\implies \bold{x = 3\%}$

Thus, for the same initial amount, the interest rate should increase by 3% such  that the simple interest would amount to 400.

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Answer 2

Step-by-step explanation:

The rate of interest, R = 5%

Time period, T = 4 years

The total amount after 4 years = Rs. 1500

To find:

(i) How much was the amount deposited initially?

(ii) For the same initial amount, how should the interest rate increase such

that the simple interest would amount to 400?

Solution:

We have the formulas as:

\begin{gathered}\boxed{\bold{S.I. = \frac{PRT}{100} }}\\\\\boxed{\bold{Amount = P + S.I.}}\end{gathered}

S.I.=

100

PRT

Amount=P+S.I.

(i) Finding the amount deposited initially:

Let "P" represent the initial sum of money.

Using the above two formulas, we can write as:

A - P = \frac{PRT}{100}A−P=

100

PRT

\implies 1500 - P = \frac{P\times 5\times 4}{100}⟹1500−P=

100

P×5×4

\implies 150000 - 100P = P\times 5\times 4⟹150000−100P=P×5×4

\implies 150000 - 100P = 20P⟹150000−100P=20P

\implies 100P + 20P = 150000⟹100P+20P=150000

\implies 120P = 150000⟹120P=150000

\implies P = \frac{150000}{120}⟹P=

120

150000

\implies \bold{P = Rs.\:1250}⟹P=Rs.1250

Thus, the amount deposited initially is Rs. 1250.

(ii) Finding the increase in the rate of interest:

Let the rate of interest is increased by "x" %.

Here

The Simple interest = Rs. 400

The rate of interest = (x + 5)%

Therefore, by using the formula of simple interest, we get

400 = \frac{1250\times (x+5)\times4}{100}400=

100

1250×(x+5)×4

\implies 100 = \frac{1250\times (x+5)}{100}⟹100=

100

1250×(x+5)

\implies 10000 = 1250\times (x+5)⟹10000=1250×(x+5)

\implies 10000 = 1250x \:+\:6250⟹10000=1250x+6250

\implies 10000 - 6250 = 1250x⟹10000−6250=1250x

\implies 3750 = 1250x⟹3750=1250x

\implies x = \frac{3750}{1250}⟹x=

1250

3750

\implies \bold{x = 3\%}⟹x=3%

Thus, for the same initial amount, the interest rate should increase by 3% such that the simple interest would amount to 400.

--------------------------------------------------------------------------------------------------

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