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Question

Youn invested your money in a fixed interest savings account that earns 5.65% per year interest. How many years with simple interest will it take to double your money and how many years will it take to double your money in an account earning compound interest at a rate of 5.65% per year?

Submitted: 307 days and 21 hours ago.
Category: Math
Value: $11
Status: CLOSED
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Optional Information

Level: 12; Subject: algebra

Already Tried:
algebra for dummies book and work book

Accepted Answer

Hi,

With simple interest it will take 17 years and 8 months
With compound interest it will take 12 years and 7 months

Work is shown below.

Lets take the Simple intrest case first

Lets say you invested $100 at 5.65%. Now money to double the intrest on your principle should be $100(because it needs t double)

so SI = P*r*t/100

P=100
SI=100
r = 5.65%
t=time

so 100 = 100*5.65*t/100
t =17.70 years = 17 years and 8 months approximately

Now A= P(1+r/100)^t

A = amoount after t year including intrest = (100+100) = 200
P=Principal = $100
r = 5.65%
t=time in years

Substituting in the above equation we get
200=100*(1+5.65/100)^t
so we get
t=12.62 years = 12 years and 7 months ...

Regards
Gaurav

PS:If you like my answers you can refer your questions to me by including my name in the question.

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Expert: GS18
Pos. Feedback: 100.0 %
Accepts: 100
Answered: 5/13/2009

Engineer

Engineer with 5 years proffesional expereince

307 days and 20 hours ago.

Reply

Guarav I understand until the line 200=100*(1+5.65/100)^t

 

if you work that out I get 200=100+5.65/100)^t

200=105.65/100t

doesnt equal 12.62 years --could you help me understand---thanks

 

 

Posted by GS18 307 days and 20 hours ago.

Info Request

Hi,

it not 200=100+5.65/100)^t

it is
200=100[1+(5.65)/100]^t
200/100=[1+0.0565]^t
2=(1.0565)^t
solving this we get
t=12.62.

Regards
Gaurav

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