First we must know that the bank rate of interest is compound and is annual. A certain amount is paid monthly, we can presume that this is fixed per month. To start we must define some terms;
At the start the total amount to be paid is the total amount borrowed since no interest has yet to be accumulated. In other words after months the amount to be paid back is what was borrowed, hence
Now after the first month, interest has been added. The value of the interest for the first month is the monthly rate of interest multiplied by the initial value of the loan. Also some of the loan is paid back after the first month and so from our definitions
After the second month, more interest has been added. The value of the interest added for the second month is the monthly rate of interest multiplied by the amount needed to be paid back after the first month. Again some of the loan is paid back, hence
From it becomes clear that
The third month follows the same procedure and so
Using and rearranging some we arrive at
So we can conjecture that
We can prove this by induction, but for this purpose we will assume it to be true. Now
is a Geometric Progression with and so
So this is the formula for the amount needed to be paid back after n months. Clearly after a certain number of months, say , all will need to be paid back and so and thus
We know that . We also know that after years or months all of the loan plus the interest must be paid back and so . Also the rate of interest is % annually which is % monthly and so
hence the amount needed to be paid monthly is
The total amount to be paid is therefore the amount needed to be paid monthly multiplied by the number of months which is approximately equal to
Inflation would not affect the amount of interest paid directly. Note that the this interest is fixed at an annual rate of %. However, that being said inflation may have an indirect impact as inflation tends to lead to wage rate increases which will lead to higher nominal incomes and thus meaning that consumers may decide to pay more back monthly since as a proportion of total income, the amount paid back on this loan will decrease.
Hope this helps.