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.