DEFINITION

Flat rate of interest measures the amount of interest per unit of loan per year.
If, for a \(10\) year loan of \(\$100000\) the total repayment is \(\$150000\) then clearly the total interest is \(50\ \%\) of the loan, which means a flat interest rate of \(5\ \%\) per year.
Flat rates of interest are used for flat rate lending more generally in informal credit sectors.

**CALCULATOR**

**Enter the following details:**

**FORMULA AND DERIVATION**

As defined above, the flat rate of interest is the total interest paid on a loan, expressed as a percentage of the loan amount, per year.

\[Flat\ rate\ of\ interest=\ \frac{total\ interest\ paid\ }{loan\ amount\ \times term\ of\ loan\ }\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\ \frac{total\ repayment-loan\ amount}{loan\ amount\ \times term\ of\ loan\ }\]

where, the term of the loan is represented in years.

If a loan is not specified in terms of a flat rate, but in terms of a regular interest rate (or APR-Annualised Percentage Charge), the amount of each instalment could be found out and summed up to find the total repayment amount.

**EXAMPLES**

Example 1

A bank lends \(\textrm{₹}\ 100000\) to a borrower in return for monthly instalments of \(\textrm{₹}\ 1297.75\) paid for \(10\) years. The borrower wishes to know the flat rate of interest.

Here,

\(Total\ repayment=1297.75\times 12\times 10=155730\)

\(Loan\ amount\ =100000\)

\(Total\ interest=155730-100000=55730\ \)

\(Term\ of\ the\ loan=10\ years\ \ \)

\[Flat\ rate\ of\ interest=\ \frac{55730}{100000\times 10}\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =0.05573\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =5.573\%\]

This means that the borrower was paying \(\textrm{₹}\ 5573\left(5.573\ \%\ of\ 100000\right)\) per year as interest, on average, for \(10\) years.