A man borrowed a sum of money and agreed to pay it off by paying Rs. 43,800 at the end of the first year and Rs. 34,992 at the end of the second year. If the rate of compound interest is 8% per annum, the sum borrowed is Rs. ___

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A man borrowed a sum of money and agreed to pay it off by paying Rs. 43,800 at the end of the first year and Rs. 34,992 at the end of the second year. If the rate of compound interest is 8% per annum, the sum borrowed is Rs. ____.

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Detailed Solution

Concept- For the given condition, the sum borrowed is Rs.67551.44. As per the question, the man agrees to pay off the loan in 2 years, with paying Rs. 43800 at the end of 1st year and Rs. 34992 at the end of 2nd Year. This means that the summation of 43800 and 34992 would be equal to the principle amount of the loan and the interest on it at the rate of compound interest is 8% per annum for 2 years.
In case of Compound Interest,

Where, A = Final Amount i.e., (Principle + Interest).
P = Principle on which Interest in compounded
R = Rate of Compound Interest/annum
n = Time period of interest
Therefore, total amount after 2 years = Rs. (43800 + 34992)
= Rs. 78792
Now, let us consider the principle to be Rs.

Given, R = 8% per annum n = 2 years
Then, forming an equation using the formula of compound interest mentioned above in the concept section,
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