Given:
Principal P = 5300 rupees.
Annual rate of interest r = 6.5% = 0.065.
Total amount A = 6678 rupees.
Consider the formula to get the amount by simple interest.
[tex]A=P(1+rt)[/tex]
Substitute P =5300, r= 0.065 and A=6678 in the formula, we get
[tex]6678=5300(1+0.065t)[/tex]
Dividing both sides by 5300, we get
[tex]\frac{6678}{5300}=\frac{5300\mleft(1+0.065t\mright)}{5300}[/tex]
[tex]\frac{6678}{5300}=1+0.065t[/tex]
Subtracting 1 from both sides of the equation, we get
[tex]\frac{6678}{5300}-1=1+0.065t-1[/tex]
[tex]\frac{6678}{5300}-1=0.065t[/tex]
Dividing both sides by 0.065, we get
[tex](\frac{6678}{5300}-1)\times\frac{1}{0.065}=\frac{0.065t}{0.065}[/tex]
[tex](\frac{6678}{5300}-1)\times\frac{1}{0.065}=t[/tex][tex]4=t[/tex]
Hence the period = 4 years.
