A trader owes a merchant ₹9,810 due in 1 year, but the trader wants to settle the account after 6 months. If the rate of simple interest is 9% per annum, how much cash (in ₹) should he pay?

Question

Accepted Answer

The amount due after 1 year is ₹9,810, which includes the principal plus interest for 1 year at 9% per annum simple interest.

Let the principal be P.

Using the formula for simple interest:
Amount = Principal + Interest
Interest = (P × R × T) / 100

Given:
Amount after 1 year = 9,810
Rate (R) = 9% per annum
Time (T) = 1 year

So,
9,810 = P + (P × 9 × 1) / 100
9,810 = P (1 + 9/100) = P × 1.09

Therefore,
P = 9,810 / 1.09 = 9,000

Now, the trader wants to settle after 6 months (0.5 years).
Interest for 6 months = (9,000 × 9 × 0.5) / 100 = 405

Amount to be paid after 6 months = Principal + Interest = 9,000 + 405 = ₹9,405

Hence, the trader should pay ₹9,405 to settle the account after 6 months.

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