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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 fo

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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

#1
+92225
+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 Sort: ### 1+0 Answers #1 +92225 +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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