A sum of money becomes ₹13,380 after 3 years and ₹20,070 after 6 years on compound Interest. Find the sum

Sure, let's solve this step by step.

Step 1: Understand the problem The problem is about compound interest. We know that the sum becomes ₹13,380 after 3 years and ₹20,070 after 6 years. We need to find the original sum.

Step 2: Use the formula for compound interest The formula for compound interest is A = P(1 + r/n)^(nt), where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Step 3: Apply the given conditions We know that the sum becomes ₹13,380 after 3 years and ₹20,070 after 6 years. This means that the interest is compounded every 3 years. So, we can write two equations from the given conditions:

1. P(1 + r/1)^(1*3) = ₹13,380
2. P(1 + r/1)^(1*6) = ₹20,070

Step 4: Solve the equations Divide the second equation by the first equation to eliminate P and find r. Then substitute r back into the first equation to find P.

Let's do the math:

(₹20,070 / ₹13,380) = (1 + r)^3 => (1 + r) = cube root of (₹20,070 / ₹13,380) => r = cube root of (₹20,070 / ₹13,380) - 1

Substitute r back into the first equation to find P:

P = ₹13,380 / ((1 + cube root of (₹20,070 / ₹13,380))^3)

Step 5: Calculate the values Calculate the values of r and P to find the original sum.