surya has to pay back the total loan plus interest, where the interest is of rs. 441 earned at the rate of 10% compounded annually in 2 years, on the loan. had surya decided to pay it in two equal installments at same rate of interest then he would have saved rs x. find the value of x.

surya has to pay back the total loan plus interest, where the interest is of rs. 441 earned at the rate of 10% compounded annually in 2 years, on the loan. had surya decided to pay it in two equal installments at same rate of interest then he would have saved rs x. find the value of x.

**Answer:** Let’s first calculate the total amount that Surya needs to pay back after 2 years with an interest rate of 10% compounded annually:

Total loan + Interest = Total amount to be paid

Let the total loan amount be P.

So, P + 441 = P*(1+0.1)^2

P + 441 = P*1.21

0.21P = 441

P = 2100

Therefore, the total amount that Surya needs to pay back is Rs. 2541 (2100 + 441).

Now, let’s consider the scenario where Surya decides to pay back the loan in two equal installments at the same interest rate of 10% compounded annually. Let the amount of each installment be x.

After the first year, the amount he owes will be:

(1 + 0.1)*(P/2 - x)

= 1.1P/2 - x

After the second year, this amount will again increase by 10%, so the total amount he owes will be:

[1.1(1.1P/2 - x)] + (P/2 - x)

= 1.21P/2 - 2.1x

This total amount should be equal to the amount he would have paid had he not split the payment into two installments, i.e., Rs. 2541.

So, we can equate these two expressions and solve for x:

1.21P/2 - 2.1x = 2541

1.21(2100)/2 - 2.1x = 2541

1270.5 - 2.1x = 2541

2.1x = 1270.5 - 2541

2.1x = -1270.5

x = -605

However, this value of x is negative, which does not make sense in this context. Therefore, it seems there has been some mistake in the problem statement or the calculations.

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