FLAT RATE OF INTEREST
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:

Loan Amount:

Duration of loan: (years)

Number of instalments per year:

Annual effective interest rate: (%)

Flat rate of interest:

Total interest paid:

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.