A sum of Rs. x was lent at 10% p.a. for 4 years, interest compounded annually. If the difference between the compound interest for the fourth year and the third year is Rs. 847, then what is the value of x?

To solve this problem, we need to understand the formula for compound interest and how it works. 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 interest rate is 10% per annum compounded annually, r = 10/100 = 0.1 and n = 1.

The compound interest for the third year would be A3 = P(1 + r)^(3) - P and for the fourth year would be A4 = P(1 + r)^(4) - P.

The problem states that the difference between the compound interest for the fourth year and the third year is Rs. 847. So, we can set up the equation A4 - A3 = 847.

Substituting the formulas for A3 and A4 into the equation gives us:

P(1 + r)^(4) - P - [P(1 + r)^(3) - P] = 847 P(1 + 0.1)^(4) - P - [P(1 + 0.1)^(3) - P] = 847 P(1.1)^(4) - P - [P(1.1)^(3) - P] = 847 P[(1.1)^(4) - (1.1)^(3)] = 847 P[1.4641 - 1.331] = 847 P[0.1331] = 847

Solving for P (which is the value of x we're looking for) gives us:

P = 847 / 0.1331 = Rs. 6363.77

So, the value of x is approximately Rs. 6364.