A sum of money is borrowed and paid back in two annual installments of Rs.882 each allowing 5% C.I.The sum borrowed was:Rs.1680Rs.1142Rs.640Rs.1640

This problem can be solved using the formula for compound interest.

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.

However, in this case, we are given the amount (A) and we need to find the principal (P). So we need to rearrange the formula to solve for P.

P = A / (1 + r/n)^(nt)

Given that the annual installments are Rs.882 each, the total amount paid back is Rs.882 * 2 = Rs.1764.

The annual interest rate is 5%, or 0.05 in decimal form. Since the interest is compounded annually, n = 1. The time is 2 years.

Substituting these values into the formula, we get:

P = 1764 / (1 + 0.05/1)^(1*2) P = 1764 / (1.05)^2 P = 1764 / 1.1025 P = Rs.1600

So, the sum borrowed was Rs.1600. However, this option is not available in the given choices. There might be a mistake in the problem or the given choices.