₹ 100000 was invested by Mohan in a fixed deposit @ `10%` per annum at CI. However every year he has to pay `20%` tax on the compound interest. How much money does Mohan has after 3 years?

Options

A. 128414
B. 108000
C. 126079.2
D. none of these

Answer

To find out how much money Mohan has after 3 years from his investment of ₹100,000 at a compound interest rate of 10% per annum, while paying 20% tax on the compound interest, we can follow these steps:

### Step 1: Calculate the effective interest rate after tax
The nominal interest rate is 10%. Since Mohan pays 20% tax on the interest earned, we need to calculate the effective interest rate.

- Tax on interest = 20% of 10% = 0.20 * 10% = 2%
- Effective interest rate = 10% - 2% = 8%

### Step 2: Calculate the amount after 1 year
Using the effective interest rate of 8%, we can calculate the amount after the first year.

- Amount after 1 year = Principal + (Principal * Effective Interest Rate)
- Amount after 1 year = ₹100,000 + (₹100,000 * 8/100)
- Amount after 1 year = ₹100,000 + ₹8,000 = ₹108,000

### Step 3: Calculate the amount after 2 years
Now, we will use the amount after the first year as the principal for the second year.

- Amount after 2 years = Amount after 1 year + (Amount after 1 year * Effective Interest Rate)
- Amount after 2 years = ₹108,000 + (₹108,000 * 8/100)
- Amount after 2 years = ₹108,000 + ₹8,640 = ₹116,640

### Step 4: Calculate the amount after 3 years
We will use the amount after the second year as the principal for the third year.

- Amount after 3 years = Amount after 2 years + (Amount after 2 years * Effective Interest Rate)
- Amount after 3 years = ₹116,640 + (₹116,640 * 8/100)
- Amount after 3 years = ₹116,640 + ₹9,331.20 = ₹125,971.20

### Final Amount
After 3 years, the total amount Mohan has is **₹125,971.20**.

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