#### I have been paying EMI for 5 years but the principal outstanding has hardly changed. Why?

This is one question that has puzzled many of us. The answer lies in understanding how loan calculations work. Most loans are Reducing Balance loans (instead of flat interest rate loans). To understand the difference between the two methods, suggest you go through the following post.

In this post, I will focus on Reducing Balance loans and will explain calculations behind this method.

### How Reducing Balance Method Works?

Under the reducing balance method, a portion of your EMI goes towards interest payment while the remaining portion goes towards principal repayment.

4. #### Principal Outstanding at the End of the Month (i.e., Beginning of the next Month) = Principal Outstanding at the Beginning of the Month – Principal Component of the EMI

Let’s try to understand with the help of an example. Suppose you have taken a loan of Rs 50 lacs for 20 years. Let’s further assume that the rate of interest stays constant at 10% p.a. EMI for the loan is Rs 48,251. You can easily find the EMI amount 1) using our EMI Calculator, 2) by doing simple mathematical calculations or 3) using PMT function in excel.

EMI Amount = PMT (Monthly Interest Rate, No. Of Months of Repayment, Loan Amount, 0, 0) * -1

Let’s go back to interest and principal calculations.

For the First Month

Principal Outstanding at the beginning of the month= Rs 50 lacs

4. #### Principal Outstanding at the end of the month (beginning of the next month) = Rs 50 lacs – Rs 6,584 = Rs 49.93 lacs

For the Second Month

Principal Outstanding at the beginning of the month= Rs 49.93 lacs

4. #### Principal Outstanding at the end of the month (beginning of the next month) = Rs 49.93 lacs – Rs 6,639 = Rs 49.87 lacs

Here is how the payment schedule will go (assuming interest rate remains constant and there are no prepayments)

 Month Principal Outstanding at the Beginning of the Month EMI Interest Principal Repayment Principal Outstanding at the End of the Month % Loan Repaid 1 5,000,000 48,251 41,667 6,584 4,993,416 0.13% 2 4,993,416 48,251 41,612 6,639 4,986,776 0.26% 3 4,986,776 48,251 41,556 6,695 4,980,082 0.40% 4 4,980,082 48,251 41,501 6,750 4,973,331 0.53% 5 4,973,331 48,251 41,444 6,807 4,966,525 0.67% 6 4,966,525 48,251 41,388 6,863 4,959,661 0.81% 7 4,959,661 48,251 41,331 6,921 4,952,741 0.95% 8 4,952,741 48,251 41,273 6,978 4,945,762 1.08% 9 4,945,762 48,251 41,215 7,036 4,938,726 1.23% 10 4,938,726 48,251 41,156 7,095 4,931,631 1.37% 11 4,931,631 48,251 41,097 7,154 4,924,477 1.51% 12 4,924,477 48,251 41,037 7,214 4,917,263 1.65% 13 4,917,263 48,251 40,977 7,274 4,909,989 1.80% 14 4,909,989 48,251 40,917 7,335 4,902,655 1.95% 15 4,902,655 48,251 40,855 7,396 4,895,259 2.09% 16 4,895,259 48,251 40,794 7,457 4,887,802 2.24% 17 4,887,802 48,251 40,732 7,519 4,880,282 2.39% 18 4,880,282 48,251 40,669 7,582 4,872,700 2.55% 19 4,872,700 48,251 40,606 7,645 4,865,055 2.70% 20 4,865,055 48,251 40,542 7,709 4,857,346 2.85% 21 4,857,346 48,251 40,478 7,773 4,849,573 3.01% 22 4,849,573 48,251 40,413 7,838 4,841,735 3.17% 23 4,841,735 48,251 40,348 7,903 4,833,832 3.32% 24 4,833,832 48,251 40,282 7,969 4,825,863 3.48% 25 4,825,863 48,251 40,216 8,036 4,817,827 3.64% 26 4,817,827 48,251 40,149 8,103 4,809,724 3.81% 27 4,809,724 48,251 40,081 8,170 4,801,554 3.97% 28 4,801,554 48,251 40,013 8,238 4,793,316 4.13% 29 4,793,316 48,251 39,944 8,307 4,785,009 4.30% 30 4,785,009 48,251 39,875 8,376 4,776,633 4.47% 31 4,776,633 48,251 39,805 8,446 4,768,188 4.64% 32 4,768,188 48,251 39,735 8,516 4,759,671 4.81% 33 4,759,671 48,251 39,664 8,587 4,751,084 4.98% 34 4,751,084 48,251 39,592 8,659 4,742,426 5.15% 35 4,742,426 48,251 39,520 8,731 4,733,695 5.33% 36 4,733,695 48,251 39,447 8,804 4,724,891 5.50% 37 4,724,891 48,251 39,374 8,877 4,716,014 5.68% 38 4,716,014 48,251 39,300 8,951 4,707,063 5.86% 39 4,707,063 48,251 39,226 9,026 4,698,038 6.04% 40 4,698,038 48,251 39,150 9,101 4,688,937 6.22% 41 4,688,937 48,251 39,074 9,177 4,679,760 6.40% 42 4,679,760 48,251 38,998 9,253 4,670,507 6.59% 43 4,670,507 48,251 38,921 9,330 4,661,177 6.78% 44 4,661,177 48,251 38,843 9,408 4,651,769 6.96% 45 4,651,769 48,251 38,765 9,486 4,642,283 7.15% 46 4,642,283 48,251 38,686 9,565 4,632,717 7.35% 47 4,632,717 48,251 38,606 9,645 4,623,072 7.54% 48 4,623,072 48,251 38,526 9,725 4,613,347 7.73% 49 4,613,347 48,251 38,445 9,807 4,603,540 7.93% 50 4,603,540 48,251 38,363 9,888 4,593,652 8.13% 51 4,593,652 48,251 38,280 9,971 4,583,681 8.33% 52 4,583,681 48,251 38,197 10,054 4,573,628 8.53% 53 4,573,628 48,251 38,114 10,138 4,563,490 8.73% 54 4,563,490 48,251 38,029 10,222 4,553,268 8.93% 55 4,553,268 48,251 37,944 10,307 4,542,961 9.14% 56 4,542,961 48,251 37,858 10,393 4,532,568 9.35% 57 4,532,568 48,251 37,771 10,480 4,522,088 9.56% 58 4,522,088 48,251 37,684 10,567 4,511,521 9.77% 59 4,511,521 48,251 37,596 10,655 4,500,866 9.98% 60 4,500,866 48,251 37,507 10,744 4,490,122 10.20% 61 4,490,122 48,251 37,418 10,833 4,479,289 10.41% 62 4,479,289 48,251 37,327 10,924 4,468,365 10.63% 63 4,468,365 48,251 37,236 11,015 4,457,350 10.85% 64 4,457,350 48,251 37,145 11,106 4,446,244 11.08% 65 4,446,244 48,251 37,052 11,199 4,435,045 11.30% 66 4,435,045 48,251 36,959 11,292 4,423,752 11.52% 67 4,423,752 48,251 36,865 11,386 4,412,366 11.75% 68 4,412,366 48,251 36,770 11,481 4,400,885 11.98% 69 4,400,885 48,251 36,674 11,577 4,389,308 12.21% 70 4,389,308 48,251 36,578 11,674 4,377,634 12.45% 71 4,377,634 48,251 36,480 11,771 4,365,863 12.68% 72 4,365,863 48,251 36,382 11,869 4,353,994 12.92% 73 4,353,994 48,251 36,283 11,968 4,342,027 13.16% 74 4,342,027 48,251 36,184 12,068 4,329,959 13.40% 75 4,329,959 48,251 36,083 12,168 4,317,791 13.64% 76 4,317,791 48,251 35,982 12,269 4,305,521 13.89% 77 4,305,521 48,251 35,879 12,372 4,293,150 14.14% 78 4,293,150 48,251 35,776 12,475 4,280,675 14.39% 79 4,280,675 48,251 35,672 12,579 4,268,096 14.64% 80 4,268,096 48,251 35,567 12,684 4,255,412 14.89% 81 4,255,412 48,251 35,462 12,789 4,242,623 15.15% 82 4,242,623 48,251 35,355 12,896 4,229,727 15.41% 83 4,229,727 48,251 35,248 13,003 4,216,724 15.67% 84 4,216,724 48,251 35,139 13,112 4,203,612 15.93% 85 4,203,612 48,251 35,030 13,221 4,190,391 16.19% 86 4,190,391 48,251 34,920 13,331 4,177,060 16.46% 87 4,177,060 48,251 34,809 13,442 4,163,618 16.73% 88 4,163,618 48,251 34,697 13,554 4,150,064 17.00% 89 4,150,064 48,251 34,584 13,667 4,136,396 17.27% 90 4,136,396 48,251 34,470 13,781 4,122,615 17.55% 91 4,122,615 48,251 34,355 13,896 4,108,719 17.83% 92 4,108,719 48,251 34,239 14,012 4,094,707 18.11% 93 4,094,707 48,251 34,123 14,129 4,080,579 18.39% 94 4,080,579 48,251 34,005 14,246 4,066,333 18.67% 95 4,066,333 48,251 33,886 14,365 4,051,968 18.96% 96 4,051,968 48,251 33,766 14,485 4,037,483 19.25% 97 4,037,483 48,251 33,646 14,605 4,022,878 19.54% 98 4,022,878 48,251 33,524 14,727 4,008,151 19.84% 99 4,008,151 48,251 33,401 14,850 3,993,301 20.13% 100 3,993,301 48,251 33,278 14,974 3,978,327 20.43% 101 3,978,327 48,251 33,153 15,098 3,963,229 20.74% 102 3,963,229 48,251 33,027 15,224 3,948,005 21.04% 103 3,948,005 48,251 32,900 15,351 3,932,654 21.35% 104 3,932,654 48,251 32,772 15,479 3,917,175 21.66% 105 3,917,175 48,251 32,643 15,608 3,901,567 21.97% 106 3,901,567 48,251 32,513 15,738 3,885,829 22.28% 107 3,885,829 48,251 32,382 15,869 3,869,959 22.60% 108 3,869,959 48,251 32,250 16,001 3,853,958 22.92% 109 3,853,958 48,251 32,116 16,135 3,837,823 23.24% 110 3,837,823 48,251 31,982 16,269 3,821,554 23.57% 111 3,821,554 48,251 31,846 16,405 3,805,149 23.90% 112 3,805,149 48,251 31,710 16,542 3,788,608 24.23% 113 3,788,608 48,251 31,572 16,679 3,771,928 24.56% 114 3,771,928 48,251 31,433 16,818 3,755,110 24.90% 115 3,755,110 48,251 31,293 16,958 3,738,152 25.24% 116 3,738,152 48,251 31,151 17,100 3,721,052 25.58% 117 3,721,052 48,251 31,009 17,242 3,703,809 25.92% 118 3,703,809 48,251 30,865 17,386 3,686,423 26.27% 119 3,686,423 48,251 30,720 17,531 3,668,893 26.62% 120 3,668,893 48,251 30,574 17,677 3,651,216 26.98% 121 3,651,216 48,251 30,427 17,824 3,633,391 27.33% 122 3,633,391 48,251 30,278 17,973 3,615,418 27.69% 123 3,615,418 48,251 30,128 18,123 3,597,296 28.05% 124 3,597,296 48,251 29,977 18,274 3,579,022 28.42% 125 3,579,022 48,251 29,825 18,426 3,560,596 28.79% 126 3,560,596 48,251 29,672 18,579 3,542,017 29.16% 127 3,542,017 48,251 29,517 18,734 3,523,283 29.53% 128 3,523,283 48,251 29,361 18,890 3,504,392 29.91% 129 3,504,392 48,251 29,203 19,048 3,485,344 30.29% 130 3,485,344 48,251 29,045 19,207 3,466,138 30.68% 131 3,466,138 48,251 28,884 19,367 3,446,771 31.06% 132 3,446,771 48,251 28,723 19,528 3,427,243 31.46% 133 3,427,243 48,251 28,560 19,691 3,407,553 31.85% 134 3,407,553 48,251 28,396 19,855 3,387,698 32.25% 135 3,387,698 48,251 28,231 20,020 3,367,677 32.65% 136 3,367,677 48,251 28,064 20,187 3,347,490 33.05% 137 3,347,490 48,251 27,896 20,355 3,327,135 33.46% 138 3,327,135 48,251 27,726 20,525 3,306,610 33.87% 139 3,306,610 48,251 27,555 20,696 3,285,914 34.28% 140 3,285,914 48,251 27,383 20,868 3,265,046 34.70% 141 3,265,046 48,251 27,209 21,042 3,244,003 35.12% 142 3,244,003 48,251 27,033 21,218 3,222,786 35.54% 143 3,222,786 48,251 26,857 21,395 3,201,391 35.97% 144 3,201,391 48,251 26,678 21,573 3,179,818 36.40% 145 3,179,818 48,251 26,498 21,753 3,158,066 36.84% 146 3,158,066 48,251 26,317 21,934 3,136,132 37.28% 147 3,136,132 48,251 26,134 22,117 3,114,015 37.72% 148 3,114,015 48,251 25,950 22,301 3,091,714 38.17% 149 3,091,714 48,251 25,764 22,487 3,069,227 38.62% 150 3,069,227 48,251 25,577 22,674 3,046,553 39.07% 151 3,046,553 48,251 25,388 22,863 3,023,690 39.53% 152 3,023,690 48,251 25,197 23,054 3,000,636 39.99% 153 3,000,636 48,251 25,005 23,246 2,977,390 40.45% 154 2,977,390 48,251 24,812 23,439 2,953,951 40.92% 155 2,953,951 48,251 24,616 23,635 2,930,316 41.39% 156 2,930,316 48,251 24,419 23,832 2,906,484 41.87% 157 2,906,484 48,251 24,221 24,030 2,882,454 42.35% 158 2,882,454 48,251 24,020 24,231 2,858,223 42.84% 159 2,858,223 48,251 23,819 24,433 2,833,791 43.32% 160 2,833,791 48,251 23,615 24,636 2,809,155 43.82% 161 2,809,155 48,251 23,410 24,841 2,784,313 44.31% 162 2,784,313 48,251 23,203 25,048 2,759,265 44.81% 163 2,759,265 48,251 22,994 25,257 2,734,008 45.32% 164 2,734,008 48,251 22,783 25,468 2,708,540 45.83% 165 2,708,540 48,251 22,571 25,680 2,682,860 46.34% 166 2,682,860 48,251 22,357 25,894 2,656,966 46.86% 167 2,656,966 48,251 22,141 26,110 2,630,856 47.38% 168 2,630,856 48,251 21,924 26,327 2,604,529 47.91% 169 2,604,529 48,251 21,704 26,547 2,577,982 48.44% 170 2,577,982 48,251 21,483 26,768 2,551,214 48.98% 171 2,551,214 48,251 21,260 26,991 2,524,223 49.52% 172 2,524,223 48,251 21,035 27,216 2,497,008 50.06% 173 2,497,008 48,251 20,808 27,443 2,469,565 50.61% 174 2,469,565 48,251 20,580 27,671 2,441,894 51.16% 175 2,441,894 48,251 20,349 27,902 2,413,992 51.72% 176 2,413,992 48,251 20,117 28,134 2,385,857 52.28% 177 2,385,857 48,251 19,882 28,369 2,357,488 52.85% 178 2,357,488 48,251 19,646 28,605 2,328,883 53.42% 179 2,328,883 48,251 19,407 28,844 2,300,039 54.00% 180 2,300,039 48,251 19,167 29,084 2,270,955 54.58% 181 2,270,955 48,251 18,925 29,326 2,241,629 55.17% 182 2,241,629 48,251 18,680 29,571 2,212,058 55.76% 183 2,212,058 48,251 18,434 29,817 2,182,240 56.36% 184 2,182,240 48,251 18,185 30,066 2,152,175 56.96% 185 2,152,175 48,251 17,935 30,316 2,121,858 57.56% 186 2,121,858 48,251 17,682 30,569 2,091,289 58.17% 187 2,091,289 48,251 17,427 30,824 2,060,466 58.79% 188 2,060,466 48,251 17,171 31,081 2,029,385 59.41% 189 2,029,385 48,251 16,912 31,340 1,998,046 60.04% 190 1,998,046 48,251 16,650 31,601 1,966,445 60.67% 191 1,966,445 48,251 16,387 31,864 1,934,581 61.31% 192 1,934,581 48,251 16,122 32,130 1,902,451 61.95% 193 1,902,451 48,251 15,854 32,397 1,870,054 62.60% 194 1,870,054 48,251 15,584 32,667 1,837,387 63.25% 195 1,837,387 48,251 15,312 32,940 1,804,447 63.91% 196 1,804,447 48,251 15,037 33,214 1,771,233 64.58% 197 1,771,233 48,251 14,760 33,491 1,737,742 65.25% 198 1,737,742 48,251 14,481 33,770 1,703,973 65.92% 199 1,703,973 48,251 14,200 34,051 1,669,921 66.60% 200 1,669,921 48,251 13,916 34,335 1,635,586 67.29% 201 1,635,586 48,251 13,630 34,621 1,600,965 67.98% 202 1,600,965 48,251 13,341 34,910 1,566,055 68.68% 203 1,566,055 48,251 13,050 35,201 1,530,855 69.38% 204 1,530,855 48,251 12,757 35,494 1,495,361 70.09% 205 1,495,361 48,251 12,461 35,790 1,459,571 70.81% 206 1,459,571 48,251 12,163 36,088 1,423,483 71.53% 207 1,423,483 48,251 11,862 36,389 1,387,094 72.26% 208 1,387,094 48,251 11,559 36,692 1,350,402 72.99% 209 1,350,402 48,251 11,253 36,998 1,313,405 73.73% 210 1,313,405 48,251 10,945 37,306 1,276,098 74.48% 211 1,276,098 48,251 10,634 37,617 1,238,482 75.23% 212 1,238,482 48,251 10,321 37,930 1,200,551 75.99% 213 1,200,551 48,251 10,005 38,246 1,162,305 76.75% 214 1,162,305 48,251 9,686 38,565 1,123,739 77.53% 215 1,123,739 48,251 9,364 38,887 1,084,853 78.30% 216 1,084,853 48,251 9,040 39,211 1,045,642 79.09% 217 1,045,642 48,251 8,714 39,537 1,006,105 79.88% 218 1,006,105 48,251 8,384 39,867 966,238 80.68% 219 966,238 48,251 8,052 40,199 926,039 81.48% 220 926,039 48,251 7,717 40,534 885,505 82.29% 221 885,505 48,251 7,379 40,872 844,633 83.11% 222 844,633 48,251 7,039 41,212 803,420 83.93% 223 803,420 48,251 6,695 41,556 761,864 84.76% 224 761,864 48,251 6,349 41,902 719,962 85.60% 225 719,962 48,251 6,000 42,251 677,711 86.45% 226 677,711 48,251 5,648 42,603 635,107 87.30% 227 635,107 48,251 5,293 42,959 592,149 88.16% 228 592,149 48,251 4,935 43,317 548,832 89.02% 229 548,832 48,251 4,574 43,677 505,155 89.90% 230 505,155 48,251 4,210 44,041 461,113 90.78% 231 461,113 48,251 3,843 44,408 416,705 91.67% 232 416,705 48,251 3,473 44,779 371,926 92.56% 233 371,926 48,251 3,099 45,152 326,775 93.46% 234 326,775 48,251 2,723 45,528 281,247 94.38% 235 281,247 48,251 2,344 45,907 235,339 95.29% 236 235,339 48,251 1,961 46,290 189,049 96.22% 237 189,049 48,251 1,575 46,676 142,374 97.15% 238 142,374 48,251 1,186 47,065 95,309 98.09% 239 95,309 48,251 794 47,457 47,852 99.04% 240 47,852 48,251 399 47,852 (0) 100.00%

If you want to see how your repayment schedule will appear on yearly basis, let’s have a look (shown below with January 2018 start).

With each EMI, interest portion of the EMI goes down while the principal portion goes up. In the first month, you paid Rs 41,667 towards interest and Rs 6,584 towards principal. In the second month, Rs 41,612 went towards interest payment while Rs 6,639 went towards principal repayment.What Does This Tell You?

Why does this happen? This happens because principal outstanding goes down with each EMI. For instance, principal outstanding goes down to Rs 49.93 after first EMI payment. After second EMI payment, it goes down to Rs 49.87 lacs. As we have seen earlier, interest component of the EMI is a product of Principal Outstanding and monthly interest rate. As principal outstanding goes down with each EMI, interest component of the next EMI will also go down. And as the interest component of the EMI goes down, principal component of the EMI will go up.

During the earlier part of your loan tenure, a greater portion goes towards interest payment. Towards the end of the repayment schedule, a greater portion of the EMI goes towards principal repayment. You can see that even after 5 years (first 60 months) of repayment, you have repaid only 10.2% of the loan amount. In the next years (between 61st and 120th month), you will repay a further 16.78% of the principal amount back. Between 121st and 180th month, you will repay 27.61% of the principal amount back. During the last 60 months (181st and 240th month), you will repay 45.42% of the principal amount back. You can see that during the first five years, you will repay only 10.2% of the principal back i.e. Rs 5.1 lacs. During the last five years, you repaid 45.42% of the principal back i.e. Rs 22.71 lacs.

If you were wondering why your loan outstanding has not moved much despite many years of timely EMI payments, you have your answer. The pace of principal repayment increases only during the later period of your repayment schedule.

### How Will Interest Rate Movements Affect You?

When interest rate changes, you will have two options.

1. Either your EMI is increased or decreased (depending upon whether interest rate is hiked or cut)
2. Or your loan tenure is increased or decreased (depending upon whether interest rate is hiked or cut)

(2) is typically the default option.

Let’s assume interest rate is cut. Let’s see how it will impact your repayment schedule. Clearly, if the annual interest rate goes down, monthly interest rate will also go down. If the monthly interest rate goes down, interest component of the EMI goes down and the principal component goes up. As the principal component goes up, the loan gets repaid faster, effectively resulting in reduction in loan tenure.

In the above example, let’s assume the loan interest rate was cut to 9% at the end of 60th month. In this case, the loan will get repaid in 221 months (60 months already paid and 161 additional months). You will end up saving about 19 EMIs.

Alternatively, if your loan interest rate was hiked, a greater portion of the EMI will go towards interest payment and a lesser portion will be left for principal repayment. This will effectively increase your loan tenure.

In the above example, let’s assume the loan interest rate was hiked to 11% at the end of 60th month. In this case, the loan will get repaid in 267 months (60 months already paid and 207 additional months). You will end up paying an additional 27 EMIs.

### How Does Prepayment Affect You?

Clearly, prepayment reduces the principal outstanding. As principal outstanding goes down, interest component of the EMI goes down. That increases the principal component of EMI. Therefore, loan gets repaid even faster.

In the above example, let’s assume you made the pre-payment of Rs 5 lacs at the end of 60th month, the loan will get repaid in 201 months (instead of 240 as per the original schedule).

### Conclusion

The calculations are with you. If you want to understand how interest rate changes and prepayments affect your pocket, you can rely on our Home Loan EMI Calculator or these basic spreadsheet calculations to assess the impact.