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Shubham lends a sum of Rs. 5500 to Sanjay. This has to repaid within a year. Find the amount by which Shubham will suffer the loss if he lends the sum on a 10% annual rate of interest compounded half-yearly instead of a 20% rate of interest compounded yearly.

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Answer: To find the amount by which Shubham will suffer a loss, we can calculate the difference in the amounts received from Sanjay under the two interest rates and compounding periods.

Let's first calculate the amount Sanjay will repay under each scenario.

10% annual rate of interest compounded half-yearly:

In this case, the interest is compounded twice a year (every 6 months).

Formula for amount compounded half-yearly:

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

where:

A = Amount

P = Principal amount (Rs. 5500)

r = Annual interest rate (10% = 0.10)

n = Number of times interest is compounded per year (2, as it is compounded half-yearly)

t = Number of years (1 year)

A = 5500 * (1 + 0.10/2)^(2*1)

A = 5500 * (1.05)^2

A = 5500 * 1.1025

A = Rs. 6063.75

20% annual rate of interest compounded yearly:

In this case, the interest is compounded once a year.

Formula for amount compounded yearly:

A = P(1 + r)^t

where:

A = Amount

P = Principal amount (Rs. 5500)

r = Annual interest rate (20% = 0.20)

t = Number of years (1 year)

A = 5500 * (1 + 0.20)^1

A = 5500 * 1.20

A = Rs. 6600

Now, let's calculate the difference:

Loss = Amount at 20% interest - Amount at 10% interest

Loss = Rs. 6600 - Rs. 6063.75

Loss = Rs. 536.25

So, Shubham will suffer a loss of Rs. 536.25 if he lends the sum at a 10% annual rate of interest compounded half-yearly instead of a 20% rate of interest compounded yearly.

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