Mortgage: Floating rate loan tenure extension on rate increase

I am trying to figure out how my bank has implemented re-pricing on my floating rate home loan.

The original home loan was for an amount of ₹ 48 lakhs (₹ 4.8 Mn) at an annual rate of interest (RoI) of 9.25% for a tenure of 4 years (48 months/repayments). The loan was disbursed on 26-Mar-2018, and the repayment start date was 05-May-2018. The cycle date (monthly EMI date) is the 5th of every month. This implies a monthly equated payments of ₹ 1.2 lakhs.

The amortization table can be seen to be:

+-----------+---------------+----------------+------------+---------------+
|  Payment  | Interest Paid | Principal Paid |  Balance   | Payment Dates |
+-----------+---------------+----------------+------------+---------------+
| 120018.82 | 37000         | 83018.82       | 4716981.18 | 2018-05-05    |
| 120018.82 | 36360.06      | 83658.75       | 4633322.43 | 2018-06-05    |
| 120018.82 | 35715.19      | 84303.62       | 4549018.8  | 2018-07-05    |
| 120018.82 | 35065.35      | 84953.46       | 4464065.34 | 2018-08-05    |
| 120018.82 | 34410.5       | 85608.31       | 4378457.03 | 2018-09-05    |
| 120018.82 | 33750.61      | 86268.21       | 4292188.82 | 2018-10-05    |
| 120018.82 | 33085.62      | 86933.2        | 4205255.62 | 2018-11-05    |
| 120018.82 | 32415.51      | 87603.31       | 4117652.32 | 2018-12-05    |
| 120018.82 | 31740.24      | 88278.58       | 4029373.73 | 2019-01-05    |
| 120018.82 | 31059.76      | 88959.06       | 3940414.67 | 2019-02-05    |
| 120018.82 | 30374.03      | 89644.79       | 3850769.89 | 2019-03-05    |
| 120018.82 | 29683.02      | 90335.8        | 3760434.09 | 2019-04-05    |
| 120018.82 | 28986.68      | 91032.14       | 3669401.95 | 2019-05-05    |
| 120018.82 | 28284.97      | 91733.84       | 3577668.1  | 2019-06-05    |
| 120018.82 | 27577.86      | 92440.96       | 3485227.15 | 2019-07-05    |
| 120018.82 | 26865.29      | 93153.52       | 3392073.62 | 2019-08-05    |
| 120018.82 | 26147.23      | 93871.58       | 3298202.04 | 2019-09-05    |
| 120018.82 | 25423.64      | 94595.18       | 3203606.86 | 2019-10-05    |
| 120018.82 | 24694.47      | 95324.35       | 3108282.51 | 2019-11-05    |
| 120018.82 | 23959.68      | 96059.14       | 3012223.37 | 2019-12-05    |
| 120018.82 | 23219.22      | 96799.6        | 2915423.78 | 2020-01-05    |
| 120018.82 | 22473.06      | 97545.76       | 2817878.02 | 2020-02-05    |
| 120018.82 | 21721.14      | 98297.67       | 2719580.34 | 2020-03-05    |
| 120018.82 | 20963.43      | 99055.39       | 2620524.96 | 2020-04-05    |
| 120018.82 | 20199.88      | 99818.94       | 2520706.02 | 2020-05-05    |
| 120018.82 | 19430.44      | 100588.38      | 2420117.65 | 2020-06-05    |
| 120018.82 | 18655.07      | 101363.74      | 2318753.9  | 2020-07-05    |
| 120018.82 | 17873.73      | 102145.09      | 2216608.81 | 2020-08-05    |
| 120018.82 | 17086.36      | 102932.46      | 2113676.35 | 2020-09-05    |
| 120018.82 | 16292.92      | 103725.9       | 2009950.46 | 2020-10-05    |
| 120018.82 | 15493.37      | 104525.45      | 1905425.01 | 2020-11-05    |
| 120018.82 | 14687.65      | 105331.17      | 1800093.84 | 2020-12-05    |
| 120018.82 | 13875.72      | 106143.09      | 1693950.75 | 2021-01-05    |
| 120018.82 | 13057.54      | 106961.28      | 1586989.47 | 2021-02-05    |
| 120018.82 | 12233.04      | 107785.77      | 1479203.7  | 2021-03-05    |
| 120018.82 | 11402.2       | 108616.62      | 1370587.07 | 2021-04-05    |
| 120018.82 | 10564.94      | 109453.88      | 1261133.2  | 2021-05-05    |
| 120018.82 | 9721.24       | 110297.58      | 1150835.62 | 2021-06-05    |
| 120018.82 | 8871.02       | 111147.79      | 1039687.82 | 2021-07-05    |
| 120018.82 | 8014.26       | 112004.56      | 927683.27  | 2021-08-05    |
| 120018.82 | 7150.89       | 112867.93      | 814815.34  | 2021-09-05    |
| 120018.82 | 6280.87       | 113737.95      | 701077.39  | 2021-10-05    |
| 120018.82 | 5404.14       | 114614.68      | 586462.71  | 2021-11-05    |
| 120018.82 | 4520.65       | 115498.17      | 470964.54  | 2021-12-05    |
| 120018.82 | 3630.35       | 116388.47      | 354576.08  | 2022-01-05    |
| 120018.82 | 2733.19       | 117285.63      | 237290.45  | 2022-02-05    |
| 120018.82 | 1829.11       | 118189.7       | 119100.75  | 2022-03-05    |
| 120018.82 | 918.07        | 119100.75      | 0          | 2022-04-05    |
+-----------+---------------+----------------+------------+---------------+

The price was subsequently revised 4 times in 2018:

+-----------------+-------------------+-------------------+
| Reschedule Date | Old Interest Rate | New Interest Rate |
+-----------------+-------------------+-------------------+
| 05-05-2018      | 9.25              | 9.47              |
| 05-07-2018      | 9.47              | 9.9               |
| 05-09-2018      | 9.9               | 10.15             |
| 05-11-2018      | 10.15             | 10.65             |
+-----------------+-------------------+-------------------+

In order to understand the impact of this re-scheduling of the loan parameters on the payments that I would have to make, I basically computed the EMIs at the new rates from the dates that the new rates became effective, with the balance tenure and the outstanding balance:

+-----------+---------------+----------------+------------+---------------+--------+---------------------+-------------------+-------------+-------------+
|  Payment  | Interest Paid | Principal Paid |  Balance   | Payment Dates |  Rate  | Pre-Payment Balance | Remaining Periods |  EMI (PIT)  | Difference  |
+-----------+---------------+----------------+------------+---------------+--------+---------------------+-------------------+-------------+-------------+
| 120018.82 | 37000         | 83018.82       | 4716981.18 | 2018-05-05    | 0.0947 | 4800000             |                48 | 120522.3017 | 503.4816561 |
| 120018.82 | 36360.06      | 83658.75       | 4633322.43 | 2018-06-05    | 0.0947 | 4716981.18          |                47 | 120512.6821 | 493.8621063 |
| 120018.82 | 35715.19      | 84303.62       | 4549018.8  | 2018-07-05    | 0.099  | 4633322.42          |                46 | 121452.8217 | 1434.001693 |
| 120018.82 | 35065.35      | 84953.46       | 4464065.34 | 2018-08-05    | 0.099  | 4549018.8           |                45 | 121424.1085 | 1405.288486 |
| 120018.82 | 34410.5       | 85608.31       | 4378457.03 | 2018-09-05    | 0.1015 | 4464065.34          |                44 | 121927.2331 | 1908.413061 |
| 120018.82 | 33750.61      | 86268.21       | 4292188.82 | 2018-10-05    | 0.1015 | 4378457.03          |                43 | 121887.1568 | 1868.336761 |
| 120018.82 | 33085.62      | 86933.2        | 4205255.62 | 2018-11-05    | 0.1065 | 4292188.82          |                42 | 122869.7364 | 2850.916363 |
| 120018.82 | 32415.51      | 87603.31       | 4117652.32 | 2018-12-05    | 0.1065 | 4205255.63          |                41 | 122806.756  | 2787.935967 |
| 120018.82 | 31740.24      | 88278.58       | 4029373.73 | 2019-01-05    | 0.1065 | 4117652.31          |                40 | 122743.614  | 2724.794047 |
| 120018.82 | 31059.76      | 88959.06       | 3940414.67 | 2019-02-05    | 0.1065 | 4029373.73          |                39 | 122680.3118 | 2661.491817 |
| 120018.82 | 30374.03      | 89644.79       | 3850769.89 | 2019-03-05    | 0.1065 | 3940414.68          |                38 | 122616.8493 | 2598.029337 |
| 120018.82 | 29683.02      | 90335.8        | 3760434.09 | 2019-04-05    | 0.1065 | 3850769.89          |                37 | 122553.226  | 2534.406029 |
| 120018.82 | 28986.68      | 91032.14       | 3669401.95 | 2019-05-05    | 0.1065 | 3760434.09          |                36 | 122489.4426 | 2470.622561 |
| 120018.82 | 28284.97      | 91733.84       | 3577668.1  | 2019-06-05    | 0.1065 | 3669401.94          |                35 | 122425.4987 | 2406.678677 |
| 120018.82 | 27577.86      | 92440.96       | 3485227.15 | 2019-07-05    | 0.1065 | 3577668.11          |                34 | 122361.3958 | 2342.575825 |
| 120018.82 | 26865.29      | 93153.52       | 3392073.62 | 2019-08-05    | 0.1065 | 3485227.14          |                33 | 122297.1325 | 2278.312479 |
| 120018.82 | 26147.23      | 93871.58       | 3298202.04 | 2019-09-05    | 0.1065 | 3392073.62          |                32 | 122232.7102 | 2213.890234 |
| 120018.82 | 25423.64      | 94595.18       | 3203606.86 | 2019-10-05    | 0.1065 | 3298202.04          |                31 | 122168.1287 | 2149.308697 |
| 120018.82 | 24694.47      | 95324.35       | 3108282.51 | 2019-11-05    | 0.1065 | 3203606.86          |                30 | 122103.3879 | 2084.567878 |
| 120018.82 | 23959.68      | 96059.14       | 3012223.37 | 2019-12-05    | 0.1065 | 3108282.51          |                29 | 122038.4883 | 2019.668266 |
| 120018.82 | 23219.22      | 96799.6        | 2915423.78 | 2020-01-05    | 0.1065 | 3012223.38          |                28 | 121973.4305 | 1954.610511 |
| 120018.82 | 22473.06      | 97545.76       | 2817878.02 | 2020-02-05    | 0.1065 | 2915423.78          |                27 | 121908.2138 | 1889.393787 |
| 120018.82 | 21721.14      | 98297.67       | 2719580.34 | 2020-03-05    | 0.1065 | 2817878.01          |                26 | 121842.8386 | 1824.018588 |
| 120018.82 | 20963.43      | 99055.39       | 2620524.96 | 2020-04-05    | 0.1065 | 2719580.35          |                25 | 121777.3065 | 1758.486522 |
| 120018.82 | 20199.88      | 99818.94       | 2520706.02 | 2020-05-05    | 0.1065 | 2620524.96          |                24 | 121711.6159 | 1692.795894 |
| 120018.82 | 19430.44      | 100588.38      | 2420117.65 | 2020-06-05    | 0.1065 | 2520706.03          |                23 | 121645.7683 | 1626.948318 |
| 120018.82 | 18655.07      | 101363.74      | 2318753.9  | 2020-07-05    | 0.1065 | 2420117.64          |                22 | 121579.7624 | 1560.942372 |
| 120018.82 | 17873.73      | 102145.09      | 2216608.81 | 2020-08-05    | 0.1065 | 2318753.9           |                21 | 121513.6003 | 1494.780304 |
| 120018.82 | 17086.36      | 102932.46      | 2113676.35 | 2020-09-05    | 0.1065 | 2216608.81          |                20 | 121447.2812 | 1428.461204 |
| 120018.82 | 16292.92      | 103725.9       | 2009950.46 | 2020-10-05    | 0.1065 | 2113676.36          |                19 | 121380.806  | 1361.986022 |
| 120018.82 | 15493.37      | 104525.45      | 1905425.01 | 2020-11-05    | 0.1065 | 2009950.46          |                18 | 121314.1738 | 1295.353827 |
| 120018.82 | 14687.65      | 105331.17      | 1800093.84 | 2020-12-05    | 0.1065 | 1905425.01          |                17 | 121247.3858 | 1228.565777 |
| 120018.82 | 13875.72      | 106143.09      | 1693950.75 | 2021-01-05    | 0.1065 | 1800093.84          |                16 | 121180.4417 | 1161.621706 |
| 120018.82 | 13057.54      | 106961.28      | 1586989.47 | 2021-02-05    | 0.1065 | 1693950.75          |                15 | 121113.3426 | 1094.522597 |
| 120018.82 | 12233.04      | 107785.77      | 1479203.7  | 2021-03-05    | 0.1065 | 1586989.47          |                14 | 121046.0879 | 1027.267944 |
| 120018.82 | 11402.2       | 108616.62      | 1370587.07 | 2021-04-05    | 0.1065 | 1479203.69          |                13 | 120978.6777 | 959.8577005 |
| 120018.82 | 10564.94      | 109453.88      | 1261133.2  | 2021-05-05    | 0.1065 | 1370587.08          |                12 | 120911.1142 | 892.2942471 |
| 120018.82 | 9721.24       | 110297.58      | 1150835.62 | 2021-06-05    | 0.1065 | 1261133.2           |                11 | 120843.3949 | 824.5748502 |
| 120018.82 | 8871.02       | 111147.79      | 1039687.82 | 2021-07-05    | 0.1065 | 1150835.61          |                10 | 120775.5208 | 756.7008245 |
| 120018.82 | 8014.26       | 112004.56      | 927683.27  | 2021-08-05    | 0.1065 | 1039687.83          |                 9 | 120707.4951 | 688.6750548 |
| 120018.82 | 7150.89       | 112867.93      | 814815.34  | 2021-09-05    | 0.1065 | 927683.27           |                 8 | 120639.3139 | 620.4938951 |
| 120018.82 | 6280.87       | 113737.95      | 701077.39  | 2021-10-05    | 0.1065 | 814815.34           |                 7 | 120570.979  | 552.1590302 |
| 120018.82 | 5404.14       | 114614.68      | 586462.71  | 2021-11-05    | 0.1065 | 701077.39           |                 6 | 120502.4915 | 483.6714774 |
| 120018.82 | 4520.65       | 115498.17      | 470964.54  | 2021-12-05    | 0.1065 | 586462.71           |                 5 | 120433.851  | 415.0310383 |
| 120018.82 | 3630.35       | 116388.47      | 354576.08  | 2022-01-05    | 0.1065 | 470964.55           |                 4 | 120365.06   | 346.2400367 |
| 120018.82 | 2733.19       | 117285.63      | 237290.45  | 2022-02-05    | 0.1065 | 354576.08           |                 3 | 120296.114  | 277.2939935 |
| 120018.82 | 1829.11       | 118189.7       | 119100.75  | 2022-03-05    | 0.1065 | 237290.45           |                 2 | 120227.0155 | 208.1955276 |
| 120018.82 | 918.07        | 119100.75      | 0          | 2022-04-05    | 0.1065 | 119100.75           |                 1 | 120157.7692 | 138.9491562 |
+-----------+---------------+----------------+------------+---------------+--------+---------------------+-------------------+-------------+-------------+

In this calculation, the

• Pre-Payment Balance is the outstanding balance prior to that EMI being paid, and the balance on which I have computed the EMI for the residual period, since the rates are applicable for all payments including those on the date for which the changes are made.
• Remaining Periods is the number of payments pending as per the original loan schedule.
• EMI (PIT) is the EMI computed on the basis of the new rate, the balance tenure and outstanding balance.
• Difference is the difference between the EMI as per the original schedule and the EMI as computed per this calculation.

The difference over the 48 periods for the EMIs as per the original schedule and the EMIs as per the changing rates is approximately ₹ 71K. Therefore, if the bank were to continue to collect the original EMIs as per the plan, they would need to make one residual collection of about ₹ 71K in the 49th period. Note that I have not computed the future value of the stream of differences.

However, this is not how my bank has implemented the re-pricing. They have simply added on one entire EMI in the 49th period (₹ 1.2 lakhs, as opposed to ₹ 71K).

My questions are:

1. Are my computations above the way that banks implement a re-pricing?
2. If so, why is my bank not charging me only for the residual difference, and instead charging me one whole EMI?

Thanks.

---

All the code to carry out the computations reported in this question can be found on this GitHub gist.