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Question

You invest a sum of money in an account that pays 9.03% compounded continuously. How many weeks must you leave this sum invested to double your money?

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**Question**

You invest a sum of money in an account that pays 9.03% compounded continuously. How many weeks must you leave this sum invested to double your money?

**Solution**

Let the present value be $x.

Hence the future value be $2x

hence we use the formula:

A=P*(e)^rt

where A=future value

P=present value

r=rate of interest

t=time period

e=mathematical constant=2.71828(approx)

Hence

$2x=$x *(e)^(0.0903t)

2=e^(0.0903t)

2=(2.71828)^(0.0903t)

Taking log on both sides;

log2 =0.0903 t*log 2.71828

Hence 0.0903t =(log 2/log 2.71828)

Hence t=(0.69315/0.0903)

=**7.68 years (approx)**

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