{"id":402,"date":"2018-12-28T00:25:14","date_gmt":"2018-12-27T18:55:14","guid":{"rendered":"https:\/\/srinivesh.in\/blog\/?p=402"},"modified":"2019-02-09T14:29:03","modified_gmt":"2019-02-09T08:59:03","slug":"benefits-of-compounding","status":"publish","type":"post","link":"https:\/\/srinivesh.in\/blog\/benefits-of-compounding\/","title":{"rendered":"Benefits of Compounding – Visualizing the Eighth Wonder"},"content":{"rendered":"

In popular imagination, Albert Einstein is supposed to have called compound interest as the eighth wonder of the world.\u00a0 He did not say any such thing. Nevertheless, compounding indeed is very beneficial for your financial health.\u00a0 This short post provides a few ways to visualize the effect of compounding.<\/p>\n

First, the formulae<\/h3>\n

Simple interest is calculated on the ‘principal’ – the original amount of investment. If simple interest accrues over multiple periods, it would always be calculated on the original amount of the investment.\u00a0 Simple Interest = Principal (P) x Interest rate per period (r) x Number of periods (n)\u00a0\u00a0\u00a0 This is an easy concept to understand.<\/p>\n

Per Investopedia, “Compound interest<\/strong> is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as \u201cinterest on interest.\u201d\u00a0\u00a0 Compound Interest = P [(1 + r)n<\/sup> \u2013 1], using the same variables as before.\u00a0 It is easy to notice that the multiplication operation in simple interest has been replaced by the exponential operation.<\/p>\n

In a simple interest scenario, increasing ‘r’ or increasing ‘n’ has a linear effect on the value of interest. i.e a 10% increase in either quantity would increase the final interest by 10%.\u00a0 In the compound interest scenario, a 10% increase in either would have a larger than 10% effect on the final interest.\u00a0 We would see this visually.<\/p>\n

Growth of a lump sum investment<\/h3>\n

<\/p>\n

For the period of 1 year, the effect is linear in compounding – as expected since the exponent is 1.\u00a0 Beyond that, the effect is significant.\u00a0\u00a0 For a period of 25 years,\u00a0 tripling of rate – from 4% to 12% – makes the final corpus more than six times larger.<\/p>\n

If you look down one column, say 10%,\u00a0 the interest for 10 years is 1.7 lacs. If you hold the investment for another 10 years, the interest almost quadruples to 6.33 lacs.\u00a0 All the advice that you get about starting to invest early stems from this.<\/p>\n

Breaking down the mechanics<\/h3>\n

We have seen that compounding happens because of the interest on interest.\u00a0 For the 1 lac scenario above, the interest calculations for 10% look like this:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Year<\/td>\nPrincipal<\/td>\nInterest on principal<\/td>\nInterest on Interest<\/td>\n<\/tr>\n
1<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 –<\/td>\n<\/tr>\n
2<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1,000<\/td>\n<\/tr>\n
3<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2,100<\/td>\n<\/tr>\n
4<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3,310<\/td>\n<\/tr>\n
5<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4,641<\/td>\n<\/tr>\n
6<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6,105<\/td>\n<\/tr>\n
7<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 7,716<\/td>\n<\/tr>\n
8<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 9,487<\/td>\n<\/tr>\n
9<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 11,436<\/td>\n<\/tr>\n
10<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 13,579<\/td>\n<\/tr>\n
11<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 15,937<\/td>\n<\/tr>\n
12<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 18,531<\/td>\n<\/tr>\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
13<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 21,384<\/td>\n<\/tr>\n
14<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 24,523<\/td>\n<\/tr>\n
15<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 27,975<\/td>\n<\/tr>\n
16<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 31,772<\/td>\n<\/tr>\n
17<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 35,950<\/td>\n<\/tr>\n
18<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 40,545<\/td>\n<\/tr>\n
19<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 45,599<\/td>\n<\/tr>\n
20<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 51,159<\/td>\n<\/tr>\n
21<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 57,275<\/td>\n<\/tr>\n
22<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 64,002<\/td>\n<\/tr>\n
23<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 71,403<\/td>\n<\/tr>\n
24<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 79,543<\/td>\n<\/tr>\n
25<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 1,00,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10,000<\/td>\n\u00a0\u00a0\u00a0\u00a0\u00a0 88,497<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The interest on principal stays constant as the principal is constant. The interest however is accumulated every year; the interest on interest thus keeps growing.\u00a0 In the ninth year, the interest on interest becomes larger than interest on the principal. This is one inflection point in compounding. In the 14th year, the accumulated interest on interest begins to exceed the accumulated interest on principal. This is the second inflection point.\u00a0 The inflection points would of course occur at different times for different interest (return) rates.<\/p>\n

Visualizing Interest on Interest<\/h3>\n

The visual effect of the non-linear growth of interest on interest can be quite striking.<\/p>\n

 <\/p>\n

 <\/p>\n

\"Benefits<\/p>\n

The top, purple, bar starts off small and grows in an exponential way.\u00a0 In the final corpus after 25 years, the interest on interest forms more than 70%; the simple interest forms just about 20%. Since this is a single investment, the principal bar stays flat, and the interest bar grows linearly.<\/p>\n

It is also easy to see from the picture the importance of long investment horizon. The purple bar gets progressively bigger and bigger.<\/p>\n

Impact of rate of return<\/h3>\n

We so far looked at a specific rate\u00a0 of return for a number of years.\u00a0 Let us look at a typical investor situation. One invests a small amount, say Rs 1000, every month in a product that provides monthly compounding. i.e. the interest is calculated monthly and added to the corpus. This further enhances the benefit of compounding.\u00a0 We look at the overall composition of the corpus with different rates of return.<\/p>\n

\"Benefits<\/p>\n

In a regular investment scenario like the above, the inflection points occur later than those for the lumpsum investment. However, the effects of increase in either the period or the rate of return are similar.\u00a0 A 50% increase in return – from 8% to 12% – more than doubles the overall interest – from 7 lacs to 16 lacs.<\/p>\n

A note on CAGR<\/h4>\n

To visualize the effect of compounding, it is simpler to think of a fixed income instrument – say a Recurring Deposit. Here the rate of return (interest rate) is fixed and we can use that rate throughout the return.\u00a0 However, these instruments don’t give high returns like equity products.\u00a0 Equity returns are lumpy – they are not uniform through the tenure. To make the comparison between different products easier, the CAGR is used.<\/p>\n

Per Investopedia, “Compound annual growth rate<\/a>, or CAGR, is\u00a0the mean annual growth rate of an investment over a specified period of time longer than one year.\u00a0It represents one of the most accurate ways to calculate and determine returns for individual assets, investment portfolios and anything that can rise or fall in value over time.”\u00a0\u00a0 Often equity products, particularly equity mutual funds, are perceived as compounding – this is not strictly true. Equity grows and can grow quite well. It does not really compound.\u00a0 However, to visualize the growth, you can use the compounding illustration.<\/p>\n

See Also:<\/h3>\n
    \n
  1. Teaching kids the power of compounding<\/a><\/li>\n
  2. Simple and Compound Interest<\/a><\/li>\n
  3. How do you calculate your Mutual Fund Returns: CAGR, IRR or XIRR?<\/a><\/li>\n
  4. Mutual funds and ‘compounding’<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    In popular imagination, Albert Einstein is supposed to have called compound interest as the eighth wonder of the world.\u00a0 He did not say any such thing. Nevertheless, compounding indeed is very beneficial for your financial health.\u00a0 This short post provides Read More<\/a><\/p>\n","protected":false},"author":4,"featured_media":404,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[4],"tags":[14],"class_list":["post-402","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gen","tag-compounding"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/posts\/402","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/comments?post=402"}],"version-history":[{"count":7,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/posts\/402\/revisions"}],"predecessor-version":[{"id":487,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/posts\/402\/revisions\/487"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/media\/404"}],"wp:attachment":[{"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/media?parent=402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/categories?post=402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/srinivesh.in\/blog\/wp-json\/wp\/v2\/tags?post=402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}