Personal Finance

The math you need to manage money

Aarati Krishnan | Updated on January 18, 2018 Published on July 31, 2016

Four concepts to stay on top of your personal finances

Did you hate maths as a student? Well, that shouldn’t become an impediment to managing your finances well. Managing your money doesn’t entail acing trigonometry or calculus. All you need to know is basic maths formulae and how to use them.


Is your NRI cousin boasting about the ₹10 lakh plot of land he acquired in the year 2000, that has trebled in value? No big deal. Your bank FD has probably given you a better return.

If you calculate the compounded annual growth rate (CAGR) on your cousin’s plot, it works out to 7.1 per cent. CAGR is derived from the compound interest formula you learnt at school. CAGR is equal to (amount/principal) ^ (1/no of years) minus 1, the whole number multiplied by 100. In the above example, ₹30 lakh divided by ₹10 lakh gives you the number 3. The sixteenth root of 3 gives you the decimal number 1.071. Simply subtract 1 from this and multiply by 100 and you get the CAGR of 7.1 per cent.

To quickly get to the CAGR, there’s the Rule of 72. It simply says that 72 divided by the number of years in which the investment will double, will fetch you its CAGR.

Let’s say Ponzi Corporation is offering you bonds which will double in eight-and-a-half years. Should you buy them? Well the rule of 72 tells you that the CAGR on these bonds is 8.5 per cent (72/8.5). This is only slightly more than a bank FD.

Time value

Have you ever been sold a moneyback plan by a friendly insurance agent? In a simplified Moneyback plan, you pay a premium of ₹15,000 a year for 15 years for a sum assured (life insurance) of ₹2 lakh.

If you survive, you get back the entire sum assured at the end of the 15{+t}{+h} year. Now you may believe that this is a wonderful deal. For a total premium payout of ₹2.25 lakh (₹15000 x 15), you get to enjoy both a life cover of ₹2 lakh for 15 years, plus money-back of ₹2 lakh.

But to really assess such plans, you need to factor in the time value of money. The best way to understand the time value of money is to imagine that you invested the same ₹15,000 every year in a savings account that earns 6 per cent and let it compound. So, your first instalment would earn interest for 14 years, the second one for 13 years, and so on.

This is the future value calculation. Doing it for all the 15 instalments above would fetch you ₹3.49 lakh at the end of 15 years.

That tells you that the Moneyback plan is gypping you of ₹ 1.49 lakh! You can also calculate what ₹2 lakh received after 15 years means in today’s rupees. The answer is ₹83,453, discounted at a 6 per cent rate. This is the present value.

Future value and present value calculations are based on the compound interest formula too. Future value is equal to present value x (1 plus R/100) raised to N, where R is your return and N is the number of years you invest for.

Rates versus yield

A friend of mine was thrilled when an equity fund that she owned declared a dividend of 30 per cent. But having invested ₹100,000, she was disappointed to receive a paltry dividend cheque of ₹3,750! Her mistake was confusing the dividend rate with dividend yield.

Companies and mutual funds usually declare dividend ‘rates’ when they make their profit distributions.

This is the dividend calculated on the face value of a share/unit. So, a 30 per cent dividend on an equity fund with a face value ₹10, amounts to ₹3 per unit.

However, what should really matter is not the dividend rate but the dividend yield.

The yield is the dividend divided by the actual cost/price of the share. My friend bought her fund at a NAV of ₹80 per unit. Therefore, her dividend yield is 3.8 per cent (3/80).

If a company announces a “100 per cent dividend” on a share with a face value of ₹10 and a market price of ₹1,000, the dividend yield is a pittance, at 1 per cent (₹10/₹1,000).

Pre- and post-tax yield

If you invest in debt products, you are sure to be foxed by confusing comparisons of pre- and post-tax yield. Interest from bank deposits and bonds is taxed at your income tax slab rate (10, 20 or 30 per cent with cess). Dividends from debt funds are tax-free in your hands. Interest from tax-free bonds and small savings schemes such as PPF suffer no tax. To make a correct assessment of what to buy, you need to compare returns (yield) after the taxman has had his pound of flesh.

Let’s compare the PPF to a five-year bank FD. Now, the PPF offers an 8.1 per cent interest which is tax-free. But on the 8 per cent interest from the bank FD, you will have to shell out a tax of 10.3 per cent, 20.6 per cent or 30.9 per cent, based on the tax slab you fall under (the fractions arise because of the education cess of 3 per cent). Assuming you are in the 10.3 per cent tax bracket, you will need to pay taxes of ₹0.82 on every ₹8 you receive from the bank FD.

But the simple way to get to the post-tax yield is to use the formula: Post-tax yield is equal to Return x (1 minus tax rate). On an 8 per cent interest, the post-tax yield is 7.18 per cent for a person in the 10.3 per cent tax bracket.

Tax-free bonds are often pitched to wealthy clients showcasing their fabulous ‘pre-tax’ yield. Assuming NHAI is offering tax-free bonds with an 8 per cent annual rate. Suppose you fall in the 30.9 per cent tax slab, you need to earn 11.57 per cent interest from a bank FD in order to get 8 per cent in your hands. This is the pre-tax yield.

While pre-tax yield may help you compare products, it is an optical illusion. The interest that NHAI pays you and the return you get is 8 per cent, and not 11-odd per cent.

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