Question

A certain sum of money is invested at the rate of 5% per annum compound interest,the interest is compounded annually.If the difference between the interests of third year and first year is 102.50.Find the sum.Please do it in the simplest way possible.(Answer is 20,000 in the answer key but i need the solution)​Thanks!

Answer 1

$\huge\mathcal\pink{Answer:-}$

Let the sum (Principle) = Rs. 100

C.I. of 1st year = Rs. \frac{100\times 5\times 1}{100} = Rs. 5$$

And, amount of 1st year = Rs. 100 + Rs. 5=Rs. 105$$

And, amount of 2nd year =Rs.105+Rs.5.25=Rs.110.25

⇒ The principle for 3rd year =Rs.110.25

Difference between C.L of 1st year and C.L of 3rd year =Rs.5.5125−Rs.5=Rs.0.5125

And, when the difference of interest =20,000(Ans)