Kolkata CI on rs 18000 for 2 1/2 years at 6% rate compounded half yearly​

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1. Question:

   • Calculate CI on ₹18000 for 2 1/2 years at 6% rate compounded half-yearly.

   Answer:

   • Compound Interest is ₹2866.93.

   Step-by-step explanation:

   Given that:

   • Principal = ₹18000
   • Rate = 6%
   • Time = 2 1/2 years = 5/2 years

   As we know that:

   • If CI is compounded half-yearly then, Rate = R/2, Time = 2n and Amount is:

   [tex]\sf{\circ\;Amount=Principal\left(1+\dfrac{Rate}{100}\right)^{Time}}[/tex]

   Calculating rate and time:

   • Rate = R/2 = 6/2 = 3%

   • Time = 2n = 5/2 × 2 = 5 half-years

   Substituting the values,

   [tex]\sf{Amount=18000\left(1+\dfrac{3}{100}\right)^{5}}[/tex]

   [tex]\sf{=18000\left(\dfrac{100+3}{100}\right)^{5}}[/tex]

   [tex]\sf{=18000\left(\dfrac{103}{100}\right)^{5}}[/tex]

   [tex]\sf{=18000\times1.1592740743}[/tex]

   [tex]\sf{=20866.93\;\;(approx.)}[/tex]

   Hence,

   • Amount = ₹20866.93

   Now,

   As we know that:

   Compound Interest = Amount – Principal

   = ₹(20866.93 – 18000)

   = ₹2866.93

   Hence,

   • CI = ₹2866.93

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