34 Retiring comfortably, or your life term savings plan

We’ve been talking rather glibly about retiring and having a ball (see Post 29 Retirement as “The Freedom Years”, Post 28 Managing retirement). But this sort of assumes that we’ve managed our savings and investment strategies, during our working life, sensibly. How much do we have to save to achieve this?

There are those who coast through life, spending most of what they earn, except maybe for the minimum that they have to pay into their Provident Fund or Retirement Plan (and that too is subject to what is termed “final” withdrawal for certain purposes like house purchase), and at best the amount that can be deducted from the taxable income. In India, this was Rs.100,000 under Section 80C of the income-tax act till recently, and from this year (financial 2014-15) it is Rs.150,000.  (This is also the maximum one can put into a Public Provident Fund Account or PPF in a year, which one should avail of before any other type of deposit, as the interest is entirely tax-free so far). The statutory investment into the Provident Fund used to be 6.25% of the salary (we interpret this as basic pay plus cost-of-living or “dearness” allowances). The question is, is this sufficient to build up a good “corpus” or body of savings to afford you a comfortable post-work life. Persons who live by the philosophy of spending their entire income probably have a legacy from their parents, either property or patents or bonds and deposits, that are sure to yield an endless stream of income, or they have a partner who is taking care of the savings part. We assume neither of these fortunate qualities is applicable to us.

Let me offer my own home-spun calculations. One fact of life is that we will have a limited working life, say from age 25 to 65: a maximum of forty years, during which period we hope to be pulling in a regular income. The second fact of life is that we cannot predict how long we will be around after that. There are life-expectancy tables and insurance tables, but we won’t go into that. My approach is to minimize the chances of regret in the future: you’ll not be happy if you plan to spend off all your assets by age 75, assuming that’s your life expectancy, and then you live to be say eighty-five and going strong; so I’ll assume that you will need to have enough money beyond your average life expectancy. The implication of this would be that you won’t be drawing down your capital after a certain (advanced) age, and will probably have to leave your savings to your heirs. You will be living off the interest or other income in the meanwhile.

There are many ways to invest your savings. The really smart people invest in land and other real estate, because it is a fact of life (is this fact number three, already?) that  nothing appreciates in value like land, if you buy cheap at the outset. A piece of land you buy at say 10 lakhs (one million, never mind the currency!) in an out-of-the-way place may be well worth a couple of crores (hundred million) in a few decades. Built flats may not appreciate so much, and may rise to twice the value and level off (because the building only depreciates, and the share of the land cost in each flat of a large block of flats is just a fraction). But one limitation is that an individual will have limited availability of funds to invest in buying real estate, since the financing is done by loans and mortgages, and more seriously, you may run up against a cycle of booms and busts (as thousands of mortgage owners found out to their cost in the USA in recent years), and may be unable to sell the property and realize your “capital” gains when you want. Land also doesn’t yield a steady income unless rentable buildings are built on it. So although the “Rich Dad, Poor Dad” series of books strongly recommends the ambitious to get into the real estate business (buying up foreclosed mortgages during a crash, and reselling after prices have climbed during a boom), this is no simple task for the average individual, and may also afford insufficient liquidity for the emergencies and stuff that one may meet over a lifetime.

The same problems are there with stocks or shares in companies. Maybe you did manage to pull off the trick of buying shares when the stock market indices had crashed in late 2008 (if I remember correctly), and watched with satisfaction the climb of the index from 9000 to around 18,000, but then chickened out just before the 2014 general elections because of the possibility of a hung Parliament, which would have sent the index tumbling. Such persons may have no complaints about the profits booked, but what with taxes and all, I don’t think it was materially better than a 12% bond or deposit that would double in 6 years (and there have been times when even the banks paid that much interest; although now our deposit interest rates are down to 8.5% or so).

Now to my home-spun calculations. Our objective is to build up enough capital to be able to live off the interest income, assuming for the present a 10% compound rate of interest for ease of calculations (!). Let us do the computations for a basic expenditure requirement unit of 10,000 a month , or 120,000 a year (we can always scale it up by whatever factor we wish later). At 10% rate of interest, and ignoring income taxes, a simple calculation tells us that we will need a capital of ten times 120,000, or 12 lakhs (1.2 million). If we feel that 10,000 a month is  too low, and that we need at least 20,000 a month, then we need to double the corpus to around 24 lakhs or 2.4 million. But don’t get the idea that it’s all we will need, because there is another factor called inflation that will stymie our well-laid plans.

How do we build up a capital of say 1.2 million at today’s prices (we can scale up by any factor later)? We assume a working life of say 30 years. There are mathematical formulae which give the cumulative value of a monthly deposit maintained over a number of years at a given interest rate (after taxes). A very simple calculation can be made by assuming an annual investment (after all, one has to save up to invest!) over 30 years, and a 10% interest rate. Here is where the great and astounding power of compound interest comes into play. The first year’s deposit, say of A, would amount to 1.1 times A after one year, then 1.1 times 1.1 A or 1.21 in the second year, and so on. Its cumulative value at the end of 30 years would be A multiplied by 1.1 times 1.1 times 1.1,, and so on 30 times, or 1.1 raised to the power 30, which we used to do with logarithms but which we can do on a calculator or spreadsheet now.

Future Value of a single investment of A at 10% rate of compound interest, assuming the saving is invested at end of year,

A₃₀ = A (1.1)²⁹ = A (15.86).

That is, our first year’s investment of A is worth 15.86 times A at the target date of our retirement. If we put in 120,000 or 1.2 lakhs in the first year, that would amount to 19,03,200 or 19.03 lakhs (1.9 million). Assuming the banks are still around and still paying interest at 10%, that corpus will give us an annual income of 1.9 lakhs (190,000), which is even higher than the principal we paid in, 120,000.

But hold your horses; we didn’t factor in inflation. If prices were to rise by some percentage every year, obviously the 190,000 we are expecting to get as interest at the 31^st year from the cumulated value of our first year’s deposit, will be much less in today’s currency. For all we know, prices may also rise at 10% every year, effectively nullifying the interest cumulated. Then at today’s prices, we would have to say that the 120,000 we put in at Year 1, remained more or less the same at the 30^th year as well. Then our annual income from this corpus would only be worth 12,000 in today’s prices (or what is termed the real value of money at constant prices), which means a monthly income of only 1000. Thus our investment of 10,000 a month is guaranteeing us only an interest of 1000 a month in today’s prices, if we allow it to cumulate without touching the interest.

If we are more fortunate, and the inflation rate is only half the interest rate, so 5% per annum (compounded), then the effective value would be calculated by discounting the Future Value at 5%. The rate of real compounding is not quite 10-5=5%, but is arrived at from the cumulative discounted real value of one year, the ratio (1.1)/(1.05)=1.0476, which implies a growth rate of 4.76% per annum, rather than 5%.  If we assume 5% for simplicity, then the Future Value of a sum A invested at the end of year 1 would be (1.05) to the power 29, or 4.12 times (contrasted with 15.86 times at 10% compound interest). A year-end deposit of 120,000 would amount in year 30 to around 494,400, in real terms (since we’ve taken out the effect of inflation!), and the annual income at that time at 10% interest rate would be 49,440. The monthly income would, of course, be one-twelfth of this, or 4120, or less than half what we put in (in real terms). 

This suggests two things. Firstly, when we put savings into fixed deposits, it is not certain at what percentage they will grow in real terms. If inflation more or less neutralizes interest, then we will be lucky to have at least the original value surviving to the future (in real or constant prices). Secondly, if we assume for convenience that this is the case, then since our income will be one-tenth the principle at 10% interest rate, it is apparent that our savings corpus will have to be around ten times the income we want in today’s prices (or more, if interest rate is going to be less than 10%). This gives us a rule of thumb to judge how much our corpus should be by retirement time at expected inflation rates (equal, in our scenario, to the long-term interest rates).

If we stick with our basic consumption requirement of 10,000 a month or 120,000 a year, our capital needs to be 12,00,000 today to provide such an income (at 10% return). At 10% inflation rate, this needs to be A (1.1)³⁰  = 17.5 times  this or 210 lakhs (21 million) in Year 30 to provide an income stream of the same purchasing power or value. Obviously this is going to be built up by putting by amounts every year, not just in Year 1. If we put by 120,000 every year, we will have, by Year 30,  a series of compounded values, thus (assuming A is invested at the end of each year)

Future Value of annual investments A over 30 years = A (1.1)²⁹+ A(1.1)²⁸+ …+A(1.1)²+A(1.1)+ A

There are formulae to calculate such series without going into `calculation of each term. Just for interest, the series given above has a total future value of A [(1.1³⁰—1)/0.1], or A[(17.5-1)/0.1], or A [165]. That is, putting aside every year 120,000 in 10% deposits, will accumulate to 165 times this or 198 lakhs (19.8 million), which will yield at that time an annual income of 19.8 lakhs (10% interest), which in real terms (at 10% inflation rate) is equivalent to 19.8/(1.1)³⁰, or 113,100. This is shy of our original 120,000 because we assumed the investment to be done at the end of the year. To get the desired corpus of 210 lakhs by Year 30, we will have to invest a little more than 10,000 a month, or we can gradually increase the monthly or annual instalments according to some formula.

Actually, we need not be limited to this amount of 10,000 per month, which frankly is a rock-bottom figure. However, if starting salaries for an average graduate are around 20,000, and if he or she is able to meet expenses with say 10,000, then the remaining 10,000 if invested regularly in fixed deposits (every month over the next 30 years), should yield an income after 30 years of  today’s 120,000 as calculated above, with only a marginal reduction in expenditure. The more the savings at early stages, the faster will the corpus grow due to the power of compound interest. If family responsibilities and rent expenses are low in the initial years, this will be an opportunity to put by larger amounts.

In the real world, of course, salaries will also gradually rise along with inflation. Even if we were to assume that we would be in a similar salary band, the starting salary of 20,000 we assumed above would definitely not remain static. It would be likely to rise itself at something close to the general price rise.  In that case, we could well reach the target of 210 lakhs (21 m) in Year 30 by starting a little lower and working up the band.  In the above formula, instead of an unchanging amount A every year, if we assume that the amount invested itself is increased 10% every year, that is 1.1 times, that adds on as an extra multiplying term:

Future Value of annual investments increasing at 10% starting at A over 30 years
= A (1.1)²⁹+ A(1.1)(1.1)²⁸+ A(1.1) ²(1.1)²⁷+…+A(1.1) ²⁷ (1.1)² +A(1.1)²⁸ (1.1)⁰¹ + A(1.1) ²⁹ (1.1)⁰

= A (1.1)²⁹+ A(1.1)²⁹+ A(1.1)²⁹+…A(1.1)²⁹

= 30A (1.1)²⁹, a cumulative saving of 30 times 15.86 or 476 times A (the power is 29, not 30, because we take each year’s investment at the end of the year; if we take full 30 years interest, the number would be 525). For maintaining our future income from interest at Year 30 at A (which we assumed is 10,000 at Year 1), we needed only 165 times A (at 10% interest rate, 10% inflation rate). This gives us a hint at the possibility of back-calculating the annual investment A we will need to maintain a desired level of income from savings alone. If annual savings also are assumed to rise at the rate of 10%, then we can get by with an annual saving (an annuity!) of 165/476 or one-third of A. In our original scenario, we assumed that A was 10,000 or one-half of our income at Year 1. If all these percentage assumptions are reasonable, we need to save only 3400 or one-sixth of our income – about 16% to 17%, not as low as the minimum provident fund level of 6.25%, which is one-sixteenth, but definitely not as demanding as the 50% saving rate we posited at the start. 

But what it also suggests is that if incomes are expected to rise at a lower rate than inflation, then the savings will have to be a higher proportion of earnings, not just 16-17%. This is a challenge, and can be maintained only by conditioning the mind to see the salary in net-of-saving terms: we pay the future ourselves first, in effect, and that part of the income is simply not money in hand (disposable income)!

Just for our interest, what if we are able to increase our annual investments A by only 5% from year to year (rather than the 10% assumed above)? The multiplying factor becomes 1.05:

Future Value of annual investments increasing at 5% starting at A at year-end
= A (1.1)²⁹+ A(1.05)(1.1)²⁸+ A(1.05)² (1.1)²⁷+…+ A(1.05)²⁷(1.1)⁰² + A(1.05)²⁸ (1.1)⁰¹+ A(1.05)²⁹(1.1)⁰

The last term in brackets, (1.1) to power zero, is just 1. This is like the previous series of 30 terms, A (1.1)²⁹+ A (1.1)²⁸+…+ A(1.1)⁰¹ + A, except that the last term is A(1.05)²⁹  instead of A, and the multiplying factor from last term to first term is  (1.1)/(1.05) = 1.048, instead of just (1.1). Putting these alternate values in the formula for total future value, A [(1.1)³⁰—1)/(0.1)], we get the formula A(1.05)²⁹ [(1.048)³⁰-1)/0.0476], or A (4.12)[(4.04-1)/0.0476] = A(4.12)[63.87] =A(263). 

I have this great book (Saving for Retirement, by Paul Westbrook, Wiley, 2003) that gives a Table 6.2 (one of many!) of precisely this sort of series. For a 30-year time horizon, at 10% rate of interest, if the annual investment A increases 5% from year to year, it gives the cumulative value as 275.68 (say, 276) times A, the difference from my calculation above (263) being perhaps due to adding of first year’s interest. If we go along with 276, this will be just above half the value with 10% annual increase (525). With no increase in A, we needed to put aside 10,000 a month or half our starting salary to achieve the desired corpus of 175A at Year 30; now that our corpus will grow to a bigger size 276A, we can make do with a smaller investment, that is 175/276 or 0.63 of the previous figure. Instead of 10,000 a month or half our assumed salary, we need to invest 6300 which is 31.5% or just short of one-third our salary, rather than the one-sixth we arrived at with a 10% increase in investment from year to year. Much higher, of course, than the 6.25%   minimum contribution to the provident fund, which is nowhere near any reasonable level of saving and investment!

If we anticipate a longer working life, we may be able to save at a somewhat slower pace to build up the desired corpus, as the formulae will show. On the other hand, we may not be earning continuously as assumed above, so higher savings are not to be sneered at when there is some extra leeway – when liabilities are fewer, and early savings are advantageous by compounding of the interest over a longer term. Also, please be aware that interest rates are not really 10% but lower, say 8.5%, so all the calculations will throw up a higher saving rate. On the whole, it is better to err on the side of higher savings, and one will have to check the progress every year and do some course correction not to be side-swiped by unforeseen changes. 

One of the factors that made things easier for my generation was that jobs carried a guaranteed pension of 50% of the last pay drawn, which had two obvious advantages: we needed to plan for only the other half (if we wanted to make up the income to pre-retirement levels), and further the  pension was half the last pay, which usually would be the highest in our range. The person saving from the salary to build up the corpus, however, averages over the range of salaries from the start of the career (low salaries) to the end, and so doesn’t get 50% of last salary drawn unless he plans well.

Sometimes, people discourage saving because “inflation makes it worthless”. I think what they mean is that inflation takes away the interest portion. I do not see that an accumulated corpus become worthless or zero value (unless we get into a collapse of the economy and everybody’s assets are rendered worthless overnight). The fact is, that we need some way to accumulate savings. Deposits are one avenue, others are real estate, gold and other precious stuff,  stocks and shares, and a few others. All the money need not go into one type of saving, but a judicious mix is to be maintained, something in the realm of “portfolio management”. However, an early start is always advisable, and it is a mistake to think that saving cannot be done in small amounts. If one builds the habit of saving even from a salary of 15,000, at least say 5000, then when salaries get to the 50,000 or 100,000 range, it will be easier to save bigger sums; if the habit has not been built up, then any salary may look insufficient to support savings. That’s why it is probably better to think in terms of saving a proportion of salary than in absolute terms, starting from a bottom figure of 15% and working up as salaries grow in real terms.

Another way to look at it is that if we were to only save for say 10 years (a nice round number which I use all the time!), and we put in a high 50% or 10,000 a month or 120,000 a year, the interest at 10% from the 11^th year will itself more than take care of our annual investment. This is not to say that one should stop saving after 10 years (in fact, with compounded interest, even earlier), because it requires closer to 30 years to build up enough capital to attain the same stream of interest as the investments, if we take into account the real interest rate (bank rate minus inflation). However, compound interest takes care of part of the burden of saving, if we let it be ploughed back into the capital (my bank accountant makes a face if I cash in any fixed deposit, which one is forced to do to pay taxes or meet medical expenses, for instance!).

One caveat is that the stuff written above consists of some rough calculations and observations, and is only a starting point for a more professional approach, with the help of guides to financial planning. Also, one has to redo the calculations with current interest rates (around 8.5% to 9% in India), and with monthly recurrent deposits and interest compounding (where provided by the banks). In the next post, I will review some material from more qualified experts on this matter!