[tex]\underline{\bf{Question:-}}[/tex]
A certain sum amounts to $ 7200 in 2 years at 6% per annum compound interest, compounded annually. Find the sum?
[tex]\underline{\bf{Given\:that:-}}[/tex]
Principle, p = ?
Amount = 7, 200
Time period, n = 2 years
Rate of interest, r = 6 % per annum.
[tex]\underline{\bf{Equation\:used:-}}[/tex]
[tex]\sf{:\implies{Amount = P(1+\dfrac{r}{n})^{nt}}}[/tex]
[tex]\sf{:\implies{7, 200 = P(1+\dfrac{6}{100})^{2}}}[/tex]
[tex]\sf{:\implies{7, 200 = P(1+0.06)^{2}}}[/tex]
[tex]\sf{:\implies{7, 200 = P(1.06)^{2}}}[/tex]
[tex]\sf{:\implies{7, 200 = P(1.1236)}}[/tex]
[tex]\sf{:\implies{p = \dfrac{7,200}{1.1236} = 6, 407.97}}[/tex]
Therefore, the sum is 6, 407.97