Question

b) 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:-

• A certain amount was deposited into a bank account having an interest rate of 5%.
• Total amount after 4years=100.

★To find:-

• Initial amount deposited.
• For the same initial amount, how should the interest rate increase  such  that the simple interest would amount to 400?​

★Solution:-

We need to know:

$\leadsto \boxed{\sf SI = PRT/100}$

Where,

P=principle,

R = rate of interest

T = time

$\leadsto \boxed{\sf Amount = P +S.I.}$

$\leadsto \boxed{\sf R=\frac{100\times SI }{P\times T}}$

To find the initial amount deposited:-

We have,

Amount = P + SI

Amount - P = SI

[SI = PRT/100]

Amount - P= PRT/100.....(1)

Given that,

Amount = 1500;

Rate = 5

Time = 4years.

Principle = ?

Substituting these values in eqn(1):-

$:\implies \sf A-P=\frac{PRT}{100} \\\\:\implies \sf 1500-P=\frac{P(5)(4)}{100} \\\\:\implies \sf (1500 - P)\times 100 =P(5)(4)\\\\:\implies \sf 150000 - 100P = 20P\\\\:\implies \sf 150000=20P+100P\\\\:\implies \sf 150000=120P\\\\:\implies \sf P=\frac{15000\cancel{0}}{12\cancel{0}}\\\\:\implies \underline{\boxed{\sf P =Rs. 1250.}}$

Therefore,

The amount deposited initially is Rs.1250.

To find increase in rate of interest:-

Here,

S.I. =Rs. 400

P=Rs. 1250  

T= 4 years

R = ?

Substituting these values in the formula,

$:\implies \sf R=\frac{100\times SI }{P\times T}$

$:\implies \sf R=\frac{100\times 400}{1250\times 4} \\\\:\implies \sf R=\frac{1000}{125}\\\\:\implies \bold{\underline{\sf R=8.}}$

Now,

Increase in rate = 8% - 5% = 3%.

Therefore,

For the same initial amount, the increase in  interest rate  such

that the simple interest would amount to 400 is 3%.

________________

Answer 2

your answer would be 3%for the amount to 400