# EMI Moratorium Math Explained

### 22-May Update — RBI has extended EMI moratorium on all term loans by another 3 months till 31-August-2020.

The Reserve Bank of India had announced a 3-month EMI moratorium as a Covid-19 regulatory package in March 2020. In a previous post, we discussed if you should opt for such a moratorium. The crux was that, if you can afford to pay and your cashflows/income potential is not severely affected due to the lockdown, you should continue to pay your EMIs and not seek EMI relief.

A few permutations and combinations are given in the following illustration.

 Loan Amount 5,00,000 30,00,000 50,00,000 50,00,000 Interest Rate 12% 9.0% 9.0% 9.0% Remaining Tenor (months) (T) 60 120 180 240 EMI 11,122 38,003 50,713 44,986 Monthly interest rate 1.00% 0.75% 0.75% 0.75% Interest for the first month 5,000 22,500 37,500 37,500 Principal O/s at the end of first month 5,05,000 30,22,500 50,37,500 50,37,500 Interest for the second month 5,050 22,669 37,781 37,781 Principal O/s at the end of second month 5,10,050 30,45,169 50,75,281 50,75,281 Interest for the third month 5,101 22,839 38,065 38,065 Principal O/s at the end of third month* 5,15,151 30,68,008 51,13,346 51,13,346 *We could have directly come to this number = Loan Amount*(1+Monthly Interest)^3 Tenure kept constant but EMI changed EMI for the increased principal (New EMI) 11,459 38,864 51,863 46,006 Increase in EMI (A) 337 861 1,150 1,020 Total excess payment over the remaining loan tenure (A * T) 20,221 1,03,379 2,06,933 2,44,793 EMI kept constant but Tenure changed No. of EMIs required to repay the loan 62.5 124.5 188.9 256.1 No. of Extra EMIs to be paid (B) 2.52 4.48 8.90 16.13 Total Excess Payment (EMI * B) 28,009 1,70,150 4,51,335 7,25,693

I got a few enquiries about the EMI moratorium math. For instance, you are stopping EMIs for only 3 months. A Rs 50 lacs loan at 9% p.a. with remaining tenure of 15 years (case 3) will accrue interest of only Rs 1.13 lacs during these 3 months.

1. How does that increase my EMIs from 180 months to 189 months (EMI remains constant)? Why do you have to pay Rs 4.51 lacs extra for just 3 months of reprieve?
2. If the tenure is kept constant at 180 months, EMI increases by 1,150 from Rs 50,713 to Rs 51,863. Multiply that by 180 months and you have an excess payment of Rs. 2.07 lacs extra over the original schedule.

Why this difference in excess payment in the two forms of adjustments? i.e., EMI unchanged (Opt #1) and Loan tenure unchanged (Opt #2). That’s the power of compounding for you. Just that it is in reverse. And the one that harms you. You can use Excel functions like PMT and NPER or the loan calculator to get all the answers. I had discussed “How Loan EMIs are calculated and work?” in an earlier post. Still, is there a simpler way to understand this?

Let’s approach this problem from a different angle. If you don’t pay EMI for 3 months, the outstanding principal grows to Rs 51.13 lacs (50 lacs * (1+9%/12)^3), after adding the interest for the three months to the original outstanding principal of Rs 50 lacs. Let’s divide this loan amount of Rs 51.13 lacs into two parts:

1. An Original loan of Rs 50 lacs and
2. A New Loan of Rs 1.13 lacs (Rs 1,13,346 to be precise).

### EMI kept constant, but the Tenure is changed

The original EMI of Rs 50,713 is enough to square off the original loan of Rs 50 lacs in 180 months.

Since the EMI remains constant, you can assume that the two loans will be repaid in succession. First, the Original Loan is paid off in 180 months. Subsequently, the EMI goes towards settling the New loan. Well, the New Loan shouldn’t sit quietly while pay off the Original Loan. Should it? It will continue to grow in size due to accrued interest.

In the 180 months, the second loan grows to 1.13 lacs * (1+9%/12)^180 = Rs 4.35 lacs.

Once the original loan is paid, the EMI of Rs 50,713 can go towards the repayment of this loan. So, you have a loan of Rs 4.35 lacs, EMI of Rs 50,713 and interest rate of 9% p.a. How many months does it take to repay this loan? You can use the Loan Calculator to find this. You will get an answer of about 9 months. Matches exactly, doesn’t it?

### Tenure kept constant, but the EMI is changed

In this case, you will have to pay an additional EMI for the New Loan. What will be the EMI for Rs 1.13 lacs loan for 180 months and an interest rate of 9% p.a.? You can again use the loan calculator to find out.

The EMI for the New Loan shall be Rs. 1,149.63.

Since the loan tenure is constant, this EMI runs simultaneously.

Total EMI to be paid per month

= EMI for the Original Loan + EMI for the new loan

= 50, 713 + 1,149.63 = Rs. 51,863

Again, everything matches.

### Why the difference between the two cases?

In the first case (EMI constant), you don’t pay the New Loan for 15 years. And that adds to the interest cost and your eventual payout.

In the second case (Tenure constant), you pay the EMI for the New Loan from the first month. This keeps the interest cost in check.

Do note, in both the cases, the cost of the loan remains the same, i.e. 9% p.a. The difference lies in only the absolute cost.