Raji deposited Rs.80000 in a bank at 10% per annum, compounded annually for two years. She wants to keep the amount deposited at the end of the two years,  Also, the rate of interest was reduced to 6% per annum. What amount should she remove from her account to ensure that she just avoids paying the tax? Assume that her account had zero balance before she deposited Rs. 80,000. Note:To just avoid paying tax, the interest for the third year should be exactly Rs. 3000.

Raji deposited Rs.80000 in a bank at 10% per annum, compounded annually for two years. She wants to keep the amount deposited at the end of the two years,  Also, the rate of interest was reduced to 6% per annum. What amount should she remove from her account to ensure that she just avoids paying the tax? Assume that her account had zero balance before she deposited Rs. 80,000. Note:To just avoid paying tax, the interest for the third year should be exactly Rs. 3000. Correct Answer 46,800

Calculation:

To just avoid paying tax, the interest for the third year should be exactly Rs. 3000.

This interest is being calculated on the amount collected by the end of the second year i.e. just for one year.

For one year, simple and compound interest gives the same value.

Hence, let the amount that gives exactly Rs. 3000 as interest for 1 year at 6% be Rs. X.

⇒ x = 3000 × 100/6

⇒ x = 50000

Actual amount collected at 10% compounded annually for 2 years = 80000 × (1.1)2

⇒ Rs. 96,800

Hence, the amount that she should remove = 96800 – 50000

⇒ Rs. 46,800