What will be the compound interest on a sum of ₹ 7500 at 4% per annum for a period of 2 years compounded annually?

Find the amount of compound interest for Rs 7500 for 1 year at 8% per annum compounded half-yearly.

Answer

Hint: In this question it is given that we have to find the amount of compound interest for Rs 7500 for 1 year at 8% per annum compounded half-yearly. So to solve this kind of problem we need know that,
Amount= $$A=P\left( 1+\dfrac{R}{100} \right)^{nt} $$......(1)
Where,
A=Final amount
P=Principle amount
R=Rate of interest
n=Number of times interest applied per time period
t=Number of time periods elapsed
Complete step-by-step solution:
Given data,
P=7500, R=8, n= 2 half-yearly= 2 times, t= 1 year=1
Therefore, Final amount,
$$A=P\left( 1+\dfrac{R}{100} \right)^{nt} $$
  =$$7500\left( 1+\dfrac{8}{100} \right)^{2\times 1} $$
  =$$7500\left( 1+\dfrac{2}{25} \right)^{2} $$
  =$$7500\left( \dfrac{25+2}{25} \right)^{2} $$
  =$$7500\left( \dfrac{27}{25} \right)^{2} $$
  =$$7500\times \dfrac{27}{25} \times \dfrac{27}{25}$$
  =$$12\times 27\times 27$$
  = 8784.
Therefore, the amount is Rs 8784.
And the compound interest = (A - P) = Rs(8784 - 7500) = Rs 1248
Note: While solving this type of problems, always remember that the value of n is the total number of times where each time the amount is compounded and the term might be a whole year, half-year or a quarter-year etc.

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