If you are already at the end of a loan period it may or may not make sense to prepay because the amount is so less and the investment period is so short that prepaying or not is not going to save you much in savings. But mathematically, it still makes sense to prepay. Also there is this psychological aspect that you don’t have the loan anymore. Finally, some people choose to spend the bonus money instead of investing for the future. So by prepaying, we take out the unnecessary spending out of the equation :). Of course I don’t mean that everyone should always be investing. You should splurge your bonus when it makes sense. Only trying to say that if you are a habitual spender then prepaying loan may be a better option. Now on to some numbers.

First lets understand how EMI works. So, anytime you take a loan, the interest is calculated on the outstanding amount of loan. Suppose you take a loan of Rs. 1 lakh. Then assuming a 1% interest per month, you will need to pay `Rs. 1,00,000 x 1% = Rs. 1,000` as interest in the first month. If that is all you did, then, next month you have to pay the same amount as interest, since you did not reduce the outstanding loan of Rs. 1 lakh. Now, say you decide to pay a bit more instead of just the interest, like Rs. 11,000. Then you paid Rs. 1,000 of interest and Rs. 10,000 of your loan. So your outstanding loan becomes `Rs. 1,00,000 - Rs. 10,000 = Rs. 90,000`. That means, next month you need to pay only `Rs. 90,000 x 1% = Rs. 900` as interest. Again next month you could pay a bit more than your interest and as you keep doing this, eventually you would have paid out all the loan as well.

That is precisely what EMIs are doing for you except that instead of being some random number every month, they are equal every month, hence the name “equated monthly installments”. The EMI is calculated on a fixed period that you or the bank decides. As you can see from the above example, if you are paying a fixed amount of Rs. 10,000 every month, then there is less and less outstanding loan as months progress. As a result, out of the Rs. 10,000, less and less amount is going to interest. Here is example table for a loan of Rs. 5 lakhs for 4 years with 10% interest rate.

Month Loan EMI Principal Interest
0 5,00,000 12,681 8,515 4,167
1 4,91,485 12,681 8,586 4,096
2 4,82,900 12,681 8,657 4,024
46 25,049 12,681 12,473 209
47 12,576 12,681 12,576 105
48 0 12,681 12,681 0

As you will notice, you will be paying an interest of Rs. 4,167 in the first month, but as you come to the end of the loan period you will be paying only Rs. 105 towards interest. One might think they are paying such small interest, might as well not prepay the loan. However, no matter which month you look at, you can take the outstanding loan amount and imagine that is a new loan you have taken for the remaining period. Let us take the same table as above and see what is the outstanding loan after 3 years.

Month Loan EMI Principal Interest
35 1,55,628 12,681 11,384 1,297
36 1,44,243 12,681 11,479 1,202
37 1,32,764 12,681 11,575 1,106

After 3 years (36 months), your outstanding loan is Rs. 1,44,243 for the remaining 1 year left in the loan period. Now, imagine you never had any loans to start with. You want to get a loan of Rs. 1,44,243 for 1 year at 10% interest. Do you know what the EMI will be? It will be exactly Rs. 12,681 like earlier when you took a loan for 4 years and Rs. 5 lakhs. So it is not about how long you have been paying EMIs, it is about the duration. A shorter duration loan will always have less interest being paid each month. Knowing this information, would you rather prepay the loan or invest it assuming you got a bonus of Rs. 1,44,243?

The same rule applies as I explained in my earlier post, which basically says that if your anticipated investment return for the loan period is less than the interest rate that the bank is charging for the loan, then it is better to prepay the loan. Since in this example the loan period left is 1 year, the anticipated risk free return for that period will be FD rate which is about 6-7%. So it is better to pay off the loan with 10% interest on it. Suppose you got a bonus of Rs. 1 lakh, then prepaying the loan by that amount is better than investing that Rs. 1 lakhs in an FD that fetches 7%. Likewise, if you can save Rs. 10,000 extra every month, then prepaying is better.

You can check both those scenarios in this spreadsheet. If you’d like to change the numbers, you can make a copy of the spreadsheet and make changes to your own copy. Of course the advantage is very small given that the period is so small. For example, with the Rs. 1 lakh bonus, the amount of money you could save is just Rs. 1,000 in one year. Thinking practically, it does not make much difference. But if precision is the name of the game then yes prepaying is better. So if you are near the end of your loan repayment, prepaying or investing may not make a lot of difference unless the loan amount is huge.