The formula for compound interest is A = P(1 + r/n)^(nt), where:

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

Given that the difference in the amount fetched between annually and semi-annually compounded interest over two years is ₹60.25, we can set up the following equation:

P(1 + r/n)^(nt) - P(1 + r)^(t) = 60.25

Substituting the given values into the equation:

P(1 + 0.20/2)^(2*2) - P(1 + 0.20)^(2) = 60.25
P(1.10)^4 - P(1.20)^2 = 60.25
P(1.4641) - P(1.44) = 60.25
P(0.0241) = 60.25

Solving for P gives us the principal amount (the initial sum of money):

P = 60.25 / 0.0241 = ₹2500

So, the sum is ₹2500.

Question

The formula for compound interest is A = P(1 + r/n)^(nt), where:

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

Given that the difference in the amount fetched between annually and semi-annually compounded interest over two years is ₹60.25, we can set up the following equation:

P(1 + r/n)^(nt) - P(1 + r)^(t) = 60.25

Substituting the given values into the equation:

P(1 + 0.20/2)^(2*2) - P(1 + 0.20)^(2) = 60.25
P(1.10)^4 - P(1.20)^2 = 60.25
P(1.4641) - P(1.44) = 60.25
P(0.0241) = 60.25

Solving for P gives us the principal amount (the initial sum of money):

P = 60.25 / 0.0241 = ₹2500

So, the sum is ₹2500.

Knowee AI · Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where:

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

Given that the difference in the amount fetched between annually and semi-annually compounded interest over two years is ₹60.25, we can set up the following equation:

P(1 + r/n)^(nt) - P(1 + r)^(t) = 60.25

Substituting the given values into the equation:

P(1 + 0.20/2)^(2*2) - P(1 + 0.20)^(2) = 60.25
P(1.10)^4 - P(1.20)^2 = 60.25
P(1.4641) - P(1.44) = 60.25
P(0.0241) = 60.25

Solving for P gives us the principal amount (the initial sum of money):

P = 60.25 / 0.0241 = ₹2500

So, the sum is ₹2500.

A sum in invested at 20% compound interest, compounded annually. In two years it would have fetched ₹ 60.25 more if the interest was compounded half yearly. Find the sum.₹ 2000₹ 3200₹ 3000₹ 2500

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