Mortgage: Floating rate loan tenure extension on rate increase

Question

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.

Answer 1

You say "the repayment start date was 05-May-2018"; The original schedule implies a loan start date one month earlier, 05-April-2018. Hence, your balance on 05-May-2018, confirmed here:

4800000*(1 + 0.0925/12) - 120018.82 = 4716981.18

So this is using an interest rate of 9.25% from 05-April-2018.

In the recomputed schedule, you say the rate of 9.47% changes in May. So the EMI for May should be based on the rate in April, the same as above.

However, you have applied 9.47% from April to arrive at the May EMI:

s = 4800000
r = 0.0947/12
n = 48
d = (r (1 + r)^n s)/((1 + r)^n - 1) = 120522.3017

If it is your intention that the 9.47% rate should apply for the first two months (i.e. from April), and the 9.9% rate applies in month 3 & 4, etc. With the original payment amount d applied, the difference due to the rates can be calculated:-

First, confirming the payment amount

s = 4800000
r = 0.0925/12
n = 48
d = (r (1 + r)^n s)/((1 + r)^n - 1) = 120018.82

Now changing the rate, the balance b after the first 2 months is

r = 0.0947/12
x = 2
b = (d + (1 + r)^x (r s - d))/r = 4635074.15

Resetting the principal s and changing the rate; balance after 2 more months is

s = b
r = 0.099/12
x = 2
b = (d + (1 + r)^x (r s - d))/r = 4470840.55

Again, resetting the principal, etc.; balance after 2 more months is

s = b
r = 0.1015/12
x = 2
b = (d + (1 + r)^x (r s - d))/r = 4305739.35

This time calculating the balance after 42 more months. This would be the 48th month, at the end of which the original loan balance would be zero.

s = b
r = 0.1065/12
x = 42
b = (d + (1 + r)^x (r s - d))/r = 163979.67

With the rate changes there is now 163979.67 remaining to be paid.

With a further 120018.82 paid in month 49 there is still a balance of 45416.17 to pay.

x = 43
b = (d + (1 + r)^x (r s - d))/r = 45416.17

Answer 2

I haven't verified your calculation. Generally the bank doesn't give you the calculation on rate change. They generically would mention x additional payment needed.

The last EMI would be deducted for residual amount. If you are paying by cheque, it will be refunded