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Answer :
It will take about 11.33 years for 1000 taka to grow to 20000 at a 6% interest rate compounded semiannually.
To find out how many years it will take for 1000 taka to grow to 20000 at a 6% interest rate compounded semiannually, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Final amount (20000 taka in this case)
P = Principal amount (1000 taka)
r = Annual interest rate (6% or 0.06 as a decimal)
n = Number of times interest is compounded per year (2 for semiannual)
t = Number of years
Now, let's solve for t:
20000 = 1000(1 + 0.06/2)^(2*t)
Divide both sides by 1000:
20 = (1 + 0.03)^(2*t)
Take the natural logarithm (ln) of both sides:
ln(20) = ln(1.03)^(2*t)
Now, isolate t:
t = ln(20) / (2 * ln(1.03))
Using a calculator:
t ≈ 11.33 years
So, it will take approximately 11.33 years for 1000 taka to grow to 20000 at a 6% interest rate compounded semiannually.
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It will take approximately 17.1 years for 1000 taka to grow to 20000 at a 6% interest rate compounded semiannually.
To find the time it takes for an investment to grow from 1000 taka to 20000 at a 6% interest rate compounded semiannually, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial principal (1000 taka), r is the interest rate per period (6% or 0.06 as a decimal), n is the number of times interest is compounded per year (2 for semiannual), and t is the number of years.
Given:
P = 1000 taka
A = 20000 taka
r = 6% = 0.06 (as a decimal)
n = 2 (semiannual compounding)
We need to solve for t:
20000 = 1000(1 + 0.06/2) ^(2t)
20 = (1.03) ^(2t)
Take the natural logarithm of both sides:
ln(20) = 1.03) ^(2t)
Apply the property of logarithms:
ln (20) = 2t * ln(1.03)
Now solve for t:
t = ln(20) / (2 * ln(1.03))
t ≈ 17.1 (approximate to one decimal place)
It will take approximately 17.1 years for 1000 taka to grow to 20000 at a 6% interest rate compounded semiannually.
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