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Find out how many months it will take for 1000 taka to grow to 20000. Given 6% annual interest rate compounded semiannually.

Answer :

Final answer:

It will take approximately 11.55 months for 1000 taka to grow to 20000 with a 6% annual interest rate compounded semiannually.

Explanation:

To find out how many months it will take for 1000 taka to grow to 20000 with a 6% annual interest rate compounded semiannually, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

  • A is the final amount (20000 taka)
  • P is the principal amount (1000 taka)
  • r is the annual interest rate (6% or 0.06)
  • n is the number of times interest is compounded per year (2 for semiannual compounding)
  • t is the number of years (unknown)

Substituting the given values into the formula, we have:

20000 = 1000(1 + 0.06/2)^(2t)

Dividing both sides by 1000:

20 = (1 + 0.03)^(2t)

Using logarithms to solve for t:

log(20) = log((1 + 0.03)^(2t))

log(20) = 2t * log(1 + 0.03)

t = log(20) / (2 * log(1 + 0.03))

Using a calculator, we find that t is approximately 11.55 months.

Learn more about calculating compound interest here:

https://brainly.com/question/31477844

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