john has $5600 to invest. he could put his money in fixed deposit earning 3% simple interest annually or invest in a unit trust with a return equivalent to 4.5% compound interest per annum. At the end of two years he would get $180 more by investing in the unit trust.Is it true?
+118724 Simple interest
I = PRT = 5600*0.03*2=$336
FV = 5600+336=$5936
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compound int - Unit trust
FV=5600(1+0.045)^2
FV=5600*(1.045)^2
$${\mathtt{5\,600}}{\mathtt{\,\times\,}}{\left({\mathtt{1.045}}\right)}^{{\mathtt{2}}} = {\mathtt{6\,115.34}}$$ dollars
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Difference = 6115.34-6025.60
$${\mathtt{6\,115.34}}{\mathtt{\,-\,}}{\mathtt{5\,936}} = {\frac{{\mathtt{8\,967}}}{{\mathtt{50}}}} = {\mathtt{179.34}}$$
so yes the difference is almost $180
+118724 Simple interest
I = PRT = 5600*0.03*2=$336
FV = 5600+336=$5936
--------------
compound int - Unit trust
FV=5600(1+0.045)^2
FV=5600*(1.045)^2
$${\mathtt{5\,600}}{\mathtt{\,\times\,}}{\left({\mathtt{1.045}}\right)}^{{\mathtt{2}}} = {\mathtt{6\,115.34}}$$ dollars
----------------------
Difference = 6115.34-6025.60
$${\mathtt{6\,115.34}}{\mathtt{\,-\,}}{\mathtt{5\,936}} = {\frac{{\mathtt{8\,967}}}{{\mathtt{50}}}} = {\mathtt{179.34}}$$
so yes the difference is almost $180
