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?

Amount owed in 1 year = ₹9,810

Time of early payment = 6 months

Rate of interest = 9% per annum

Simple Interest (SI) = $$\frac{P \times R \times T}{100} ​$$​​

Where:

P is the principal (amount trader will pay now)

R is the rate of interest

T is the time period in years 

Solution: 

Let the principal be p 

Trader owed ₹9810 after one year 

So, A = 9810 

​$$9810 = p \left( \frac{9 \times 1}{100} + 1 \right) \\ \ \\ 9810 = p \left( \frac{9 +100}{100} \right) \\ \ \\ p = \frac{981000}{109} = 9000$$ 

So, now for 6 months trader has to pay  interest:

​$$= \frac{9000 \times 4.5 \times 1}{100} \\ \ \\ = 405$$ 

So, Total Amount Trader pays to the merchant = 9000 + 405 = ₹9405