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The compound interest on 800 at a certain rate for two years is 65.28. What would be the approximate compound interest on the same amount for three years?

Guest Jun 3, 2015

Best Answer 

 #1
avatar+90996 
+5

 

 

$$\\865.28=800(1+r)^2\\\\
865.28/800=(1+r)^2\\\\
\sqrt{865.28/800}=1+r\\\\
\sqrt{865.28/800}-1=r\\\\$$

 

$${\sqrt{{\frac{{\mathtt{865.28}}}{{\mathtt{800}}}}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\frac{{\mathtt{1}}}{{\mathtt{25}}}} = {\mathtt{0.04}}$$    

 

so the rate is 4% per annum

 

Amount after 3 years

 

FV= 800(1.04)^3

$${\mathtt{800}}{\mathtt{\,\times\,}}{\left({\mathtt{1.04}}\right)}^{{\mathtt{3}}} = {\mathtt{899.891\: \!2}}$$

 

The compound interest after 3 years will be  $99.89

 

$${\mathtt{899.89}}{\mathtt{\,-\,}}{\mathtt{800}} = {\frac{{\mathtt{9\,989}}}{{\mathtt{100}}}} = {\mathtt{99.89}}$$       

Melody  Jun 3, 2015
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1+0 Answers

 #1
avatar+90996 
+5
Best Answer

 

 

$$\\865.28=800(1+r)^2\\\\
865.28/800=(1+r)^2\\\\
\sqrt{865.28/800}=1+r\\\\
\sqrt{865.28/800}-1=r\\\\$$

 

$${\sqrt{{\frac{{\mathtt{865.28}}}{{\mathtt{800}}}}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\frac{{\mathtt{1}}}{{\mathtt{25}}}} = {\mathtt{0.04}}$$    

 

so the rate is 4% per annum

 

Amount after 3 years

 

FV= 800(1.04)^3

$${\mathtt{800}}{\mathtt{\,\times\,}}{\left({\mathtt{1.04}}\right)}^{{\mathtt{3}}} = {\mathtt{899.891\: \!2}}$$

 

The compound interest after 3 years will be  $99.89

 

$${\mathtt{899.89}}{\mathtt{\,-\,}}{\mathtt{800}} = {\frac{{\mathtt{9\,989}}}{{\mathtt{100}}}} = {\mathtt{99.89}}$$       

Melody  Jun 3, 2015

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