Math, asked by yadavloveshit, 7 months ago

If rupees 40000 amounts to rupees 46305 in 1 complete 1/2year, compound interest payable half yearly, find the rate of interest per annum​

Answers

Answered by Anonymous
3

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Answer:

Rate of interest is 10% p.a.

Step-by-step explanation:

Principal sum P = 40000

Final Amt A = 46305

No. of times interest is compounded in 1 year i.e. n = 2 (half year)

time of interest t = 1 1/2 or 3/2 yrs

So, compound interest formula we have is,

A = P [ 1 + r/n ] ^ nt      where r is rate of interest

So putting our values,

46305 = 40000 [ 1 + r/2 ] ^3     { nt = 2 x 3/2 = 3 }

9261 = 8000 [ 1 + r/2 ] ^3

9261 / 8000 = [ 1 + r/2 ] ^3

[ 21 / 20 ] ^3 = [ 1 + r/2 ] ^3

As we are calculating positive value r we can cancel the powers of 3

21/20 = 1 + r/2

r/2 = 1/20

r = 1/10 or 0.1 or 10%

Therefore, rate of interest is 10% p.a.

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Answered by RvChaudharY50
1

Given :-

  • Principal = Rs.40000
  • Amount = Rs.46305
  • Time = (3/2) years.
  • Rate = compounded half yearly .

To Find :-

  • The rate of interest per annum. ?

Solution :-

we know that, when interest is compounded half yearly ,

  • Rate becomes half .
  • Time becomes double.

so,

  • Time = (3/2) * 2 = 3 years.
  • Rate = Let half yearly is R% .

then,

→ P[1 + (R/100)]^T = A

→ 40000[1 + (R/100)]³ = 46305

→ [1 + (R/100)]³ = 46305/40000

→ [1 + (R/100)]³ = 9261/8000

→ [1 + (R/100)]³ = (21/20)³

cube root both sides,

→ 1 + (R/100) = (21/20)

→ (R/100) = (21/20) - 1

→ (R/100) = (21 - 20)/20

→ (R/100) = (1/20)

→ R = 5% .

therefore,

→ The rate of interest per annum = 5 * 2 = 10% (Ans.)

Learn more :-

CI in 2yr is Rs. 1600 and in 3 yrs it will be Rs. 1700. Find the rate of interest.

https://brainly.in/question/32463301

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