Calculation of Principal Amount

To calculate the principal amount, we will use the formula for compound interest:

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

Where,
A = Final amount (including interest)
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time (in years)

In this case, we know the following values:

r = 5% = 0.05 (as the interest rate is given as per annum)
n = 1 (as the interest is compounded annually)
t = 2 (as the loan is taken for 2 years)
A = P + CI = P(1 + r/n)^(nt) + CI = P(1 + 0.05/1)^(1*2) + 512.50

Now, we can solve for P:

P = A/(1 + r/n)^(nt) - CI = (512.50 + P)/(1 + 0.05/1)^(1*2)

Simplifying this equation, we get:

P/1.1025 = 512.50 + P

P - 1.1025P = 562.81

0.8975P = 562.81

P = 626.67

Therefore, Rahul borrowed Rs. 626.67.

Explanation

Compound interest is the interest calculated on the principal amount as well as the accumulated interest from previous periods. In this case, Rahul borrowed some money at a 5% annual interest rate for 2 years. This means that at the end of the first year, he would have to pay interest on the principal amount as well as the interest earned in the first year. This process continues for the second year as well.

The formula for compound interest takes into account the principal amount, interest rate, compounding frequency, and time period. Using this formula, we can calculate the final amount that Rahul would have to pay back, including the interest. By subtracting the compound interest from the final amount, we get the principal amount that Rahul borrowed.

In this case, the principal amount was calculated to be Rs. 626.67.

Let sum be p and
A= p(1+r/100)n
=p(1+5/100)2
=p(21/20)2
=441/400p
CI= A-P
= 441/400p-p
= 41/400p
Therefore CI= 512.50(given)
= CI=41/400p(Proved)
= 41/400p= 512.50
=p= 512.50*400/41
= p=4200rs