To solve this problem, we need to understand the concept of compound interest. Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.

Step 1: Calculate the interest for the first year, which is compounded half-yearly.

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:
P = ₹ 20000
r = 20% per annum = 0.20
n = 2 (since it's compounded half-yearly)
t = 1 year

Substitute these values into the formula:

A = 20000 (1 + 0.20/2)^(2*1)
A = 20000 (1 + 0.10)^2
A = 20000 * 1.10^2
A = 20000 * 1.21
A = ₹ 24200

The amount after the first year is ₹ 24200. The interest earned in the first year is ₹ 24200 - ₹ 20000 = ₹ 4200.

Step 2: Calculate the interest for the second year, which is compounded yearly.

Now, the principal amount for the second year is the amount accumulated after the first year, which is ₹ 24200.

Given:
P = ₹ 24200
r = 20% per annum = 0.20
n = 1 (since it's compounded yearly)
t = 1 year

Substitute these values into the formula:

A = 24200 (1 + 0.20/1)^(1*1)
A = 24200 (1 + 0.20)^1
A = 24200 * 1.20^1
A = 24200 * 1.20
A = ₹ 29040

The amount after the second year is ₹ 29040. The interest earned in the second year is ₹ 29040 - ₹ 24200 = ₹ 4840.

Step 3: Calculate the total interest earned at the end of 2 years.

The total interest earned at the end of 2 years is the sum of the interest earned in the first year and the second year.

Total interest = ₹ 4200 (first year) + ₹ 4840 (second year) = ₹ 9040.

So, the total interest earned at the end of 2 years is ₹ 9040.

Question

To solve this problem, we need to understand the concept of compound interest. Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.

Step 1: Calculate the interest for the first year, which is compounded half-yearly.

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:
P = ₹ 20000
r = 20% per annum = 0.20
n = 2 (since it's compounded half-yearly)
t = 1 year

Substitute these values into the formula:

A = 20000 (1 + 0.20/2)^(2*1)
A = 20000 (1 + 0.10)^2
A = 20000 * 1.10^2
A = 20000 * 1.21
A = ₹ 24200

The amount after the first year is ₹ 24200. The interest earned in the first year is ₹ 24200 - ₹ 20000 = ₹ 4200.

Step 2: Calculate the interest for the second year, which is compounded yearly.

Now, the principal amount for the second year is the amount accumulated after the first year, which is ₹ 24200.

Given:
P = ₹ 24200
r = 20% per annum = 0.20
n = 1 (since it's compounded yearly)
t = 1 year

Substitute these values into the formula:

A = 24200 (1 + 0.20/1)^(1*1)
A = 24200 (1 + 0.20)^1
A = 24200 * 1.20^1
A = 24200 * 1.20
A = ₹ 29040

The amount after the second year is ₹ 29040. The interest earned in the second year is ₹ 29040 - ₹ 24200 = ₹ 4840.

Step 3: Calculate the total interest earned at the end of 2 years.

The total interest earned at the end of 2 years is the sum of the interest earned in the first year and the second year.

Total interest = ₹ 4200 (first year) + ₹ 4840 (second year) = ₹ 9040.

So, the total interest earned at the end of 2 years is ₹ 9040.

Knowee AI · Accepted Answer

To solve this problem, we need to understand the concept of compound interest. Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.

Step 1: Calculate the interest for the first year, which is compounded half-yearly.

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:
P = ₹ 20000
r = 20% per annum = 0.20
n = 2 (since it's compounded half-yearly)
t = 1 year

Substitute these values into the formula:

A = 20000 (1 + 0.20/2)^(2*1)
A = 20000 (1 + 0.10)^2
A = 20000 * 1.10^2
A = 20000 * 1.21
A = ₹ 24200

The amount after the first year is ₹ 24200. The interest earned in the first year is ₹ 24200 - ₹ 20000 = ₹ 4200.

Step 2: Calculate the interest for the second year, which is compounded yearly.

Now, the principal amount for the second year is the amount accumulated after the first year, which is ₹ 24200.

Given:
P = ₹ 24200
r = 20% per annum = 0.20
n = 1 (since it's compounded yearly)
t = 1 year

Substitute these values into the formula:

A = 24200 (1 + 0.20/1)^(1*1)
A = 24200 (1 + 0.20)^1
A = 24200 * 1.20^1
A = 24200 * 1.20
A = ₹ 29040

The amount after the second year is ₹ 29040. The interest earned in the second year is ₹ 29040 - ₹ 24200 = ₹ 4840.

Step 3: Calculate the total interest earned at the end of 2 years.

The total interest earned at the end of 2 years is the sum of the interest earned in the first year and the second year.

Total interest = ₹ 4200 (first year) + ₹ 4840 (second year) = ₹ 9040.

So, the total interest earned at the end of 2 years is ₹ 9040.

A invested ₹ 20000 with the rate of interest of 20 percent per annum. The interest was compounded half-yearly for 1st year and in the next year, it was compounded yearly. Find the total interest earned at the end of 2 years? ₹ 8800₹ 9040₹ 8040₹ 9800

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