A man invests Rs.6000 for 3 years at 8% p.a. compound interest reckoned yearly. Income tax at the rate of 10% on the interest earned is deducted at the end of each year. what the amount at the end of the third year (round off the answer to the closest integer)?

Step 1: Calculate the compound interest for the first year.

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.

In this case, P = Rs.6000, r = 8% or 0.08 (in decimal), n = 1 (since interest is compounded yearly), and t = 1 (for the first year).

So, A = 6000(1 + 0.08/1)^(1*1) = Rs.6480

Step 2: Deduct the income tax.

The income tax is 10% of the interest earned. The interest earned in the first year is Rs.6480 - Rs.6000 = Rs.480.

So, the income tax = 10% of Rs.480 = Rs.48.

The amount at the end of the first year after tax deduction = Rs.6480 - Rs.48 = Rs.6432.

Step 3: Repeat the process for the next two years.

For the second year, P = Rs.6432, r = 0.08, n = 1, and t = 1.

So, A = 6432(1 + 0.08/1)^(1*1) = Rs.6946.56

The interest earned in the second year is Rs.6946.56 - Rs.6432 = Rs.514.56.

So, the income tax = 10% of Rs.514.56 = Rs.51.46.

The amount at the end of the second year after tax deduction = Rs.6946.56 - Rs.51.46 = Rs.6895.1.

For the third year, P = Rs.6895.1, r = 0.08, n = 1, and t = 1.

So, A = 6895.1(1 + 0.08/1)^(1*1) = Rs.7446.71

The interest earned in the third year is Rs.7446.71 - Rs.6895.1 = Rs.551.61.

So, the income tax = 10% of Rs.551.61 = Rs.55.16.

The amount at the end of the third year after tax deduction = Rs.7446.71 - Rs.55.16 = Rs.7391.55.

So, the amount at the end of the third year, rounded off to the closest integer, is Rs.7392.