[tex]\underline{\bf{Question:-}}[/tex]
Calculate the amount and CI on rupees 65000 for 3 years at 7.5 percentage per annum compounded annually
[tex]\underline{\bf{Given\:that:-}}[/tex]
Principle, p = 65, 000
Time period, n = 3 years
Rate of interest, r = 7.5 % per annum.
[tex]\underline{\bf{Equation\:used:-}}[/tex]
[tex]\sf{:\implies{Amount = P(1+\dfrac{r}{n})^{nt}}}[/tex]
[tex]\sf{:\implies{Compound\:Interest = P(1+\dfrac{r}{n})^{nt}-1}}[/tex]
[tex]\sf{:\implies{Amount = Principle + Compound\:Interest}}[/tex]
[tex]\underline{\bf{Solution:-}}[/tex]
[tex]\sf{\implies{Compound\:Interest = P(1+\dfrac{r}{n})^{nt}-1}}[/tex]
[tex]\sf{\implies{Compound\:Interest = 65, 000(1+\dfrac{7.5}{100})^{3}-1}}[/tex]
[tex]\sf{\implies{Compound\:Interest = 65, 000(1+0.075)^{3}-1}}[/tex]
[tex]\sf{\implies{Compound\:Interest = 65, 000[(1.075)^{3}-1]}}[/tex]
[tex]\sf{\implies{Compound\:Interest = 65, 000[1.242296-1]}}[/tex]
[tex]\sf{\implies{Compound\:Interest = 65, 000[0.242296]}}[/tex]
[tex]\sf{\implies{Compound\:Interest = 15, 749}}[/tex]
[tex]\boxed{\bf{\implies{Compound\:Interest = 15, 749}}}[/tex]
[tex]\bf{\implies{Amount = Principle + Compound\:Interest}}[/tex]
[tex]\sf{\implies{Amount = 65, 000+ 15, 749}}[/tex]
[tex]\sf{\implies{Amount = 80, 749}}[/tex]
[tex]\boxed{\bf{\implies{Amount = 80, 749}}}[/tex]
[tex]\underline{\sf{Additional\:information:-}}[/tex]
1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by
[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{n})^{nt}}}}[/tex]
Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by
[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{200})^{2n}}}}[/tex]
3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by
[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{400})^{4n}}}}[/tex]
4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by
[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{1200})^{12n}}}}[/tex]
