It is important to know some basic formulae that you can use to do your own calculations. Given below are 10 such formulae that everyone should know

Jinsy Mathhew

- November 10, 2015
- | Edition:November 22, 2015

The first step towards financial security is taking control of your finances. Money management is an art which includes saving the right amounts and investing in the right instruments. However, there are several factors such as inflation and time that lower the value of money. Therefore, it is necessary to learn how to calculate the worth of one's investments.

Several financial planning calculators are available on the web. However, it is also important to know some basic formulae that you can use to do your own calculations. Given below are 10 such formulae that everyone should know.

**1. Compound Interest **

You may have heard financial experts/advisors extol the power of compounding. Albert Einstein, in fact, called compounding "the greatest mathematical discovery of all time".

Compounding is the process of earning interest on principal as well as accumulated interest. The longer the duration of the investment, the greater is the potential for gaining from compounding, which makes it a very powerful tool in finance.

The formula is

**Formula: A = P * (1+r/t) ^ (nt)**

Where

A = amount after time t

P = principal amount (your initial investment)

r = annual interest rate (divide the number by 100)

t = number of years

n = number of times the interest is compounded per year

EXAMPLE

Suppose you intend to invest Rs 1,00,000 for 10 years at an interest rate of 10 per cent and the compounding is annual.

The total amount you will receive after 10 years will be

= 1,00,000(1+0.1) ^10 = 2,59,374.25

This shows that the interest earned over 10 years is Rs 1,59,374.25

If you were to stretch the period by another 10 years, which makes it a total of 20 years, the return would be Rs 6,72,749.99. The interesting point is that your investment grew over four times in 20 years. That is why compound interest is your best friend when it comes to investing. A longer tenure, coupled with higher frequency of compounding (quarterly, half-yearly), can work magic. So, the next time your financial adviser asks you to stay long and enjoy the ride, know that he is referring to the power of compounding.

**2. Post Tax Return **

We invest thinking about probable returns that can be generated. But we forget that these returns will be much lower if we take into account taxes too.

Continuing with the earlier example, the returns above are pre-tax. What you see on your fixed deposit certificate is the absolute figure. As per the income tax rules, any income from a bank deposit is taxable as per one's tax slab. So, if you fall in the 30 per cent tax bracket, the interest earned will fall by 30 per cent.

**Formula = Interest rate - (Interest rate*tax rate) **

= 10-(10*30%) = 7

This means that the effective interest earned after tax falls to 7 percent. It is always wise to calculate post-tax returns while investing in a financial instrument.

**3. Inflation **

Inflation lowers purchasing power of the rupee. As a result, whenever a saving plan is being chalked out, inflation is one of the factors that has to be taken into account.

EXAMPLE

It is important to know what will be the future value of, say, today's Rs 10,000, ten years later if inflation is 5%.

**Formula: Future amount = Present amount * (1+inflation rate) ^number of years**

= 10,000* (1+5%) ^10 = 16,289

The future value of present Rs 10,000 turns out to be Rs 16,289.

**4. Purchasing Power **

Conversely, if you want to determine the purchasing power of the same Rs 10,000 in future, keeping all the other parameter as before, the formula is:-

**Formula: Future Value = Present value/(1+inflation rate)^number of years**

=10,000/ (1+5%) ^10 = 6,139

The value of Rs 10,000 will decline

to Rs 6,139 in 10 years if inflation is 5 per cent.

**5. Effective Annual Rate**

Generally, an investment's annual rate of return is different from the nominal rate of return when compounding occurs more than once a year (quarterly, half-yearly). The formula for converting the nominal return into effective annual rate is:-

**Formula: Effective Annual Rate = (1+(r/n))^n)-1*100**

Where

r = nominal return divided by number of times compounding is done in a year

n = number of times compounding is done in a year

EXAMPLE

If an investment is made at 9 per cent annual rate and compounding is done quarterly, the effective annual rate will be

Effective annual rate =

(1+(0.09/4)^4) -1*100 = 9.3 per cent

Thanks to the power of compounding, the effective annual rate of the fixed deposit turns out to be 9.3 per cent

**6. Rule of 72**

Rule of 72 refers to the time value of money. It helps you know the time (in terms of years) required to double your money at a given interest rate. That's why it is popularly known as the 'doubling of money' principle.

**The thumb rule is divide 72 by the interest rate **

EXAMPLE

If you are assuming a 12 per cent return on your investment,

the number of years in which the money will double is

= 72/Interest rate= 72/12 = 6 years

**7. Compounded Annual Growth Rate (CAGR)**

This is used to indicate the return on an investment over a period. It is also the best tool to compare returns of two different asset classes - for instance gold/equity or equity/real estate.

The benefit of using this parameter is that it provides a smoothed-out return over a period, ignoring volatility.

There are three components that make up CAGR - beginning value, ending value and number of years. The equation is presented as:

**Formula: CAGR=((FV/PV)^(1/n)) - 1 **

Where

FV is the investment's ending/maturity value

PV is the investment's beginning/opening value

n is the duration in years

EXAMPLE

Case I

Suppose that an investment of Rs 1,000 grows to Rs 5,000 in 10 years.

The CAGR is calculated as ((5,000/1,000)^(1/10)) - 1

This comes to 17.4 per cent, indicating that the investment grew at a CAGR of 17.4 per cent over the period.

Case II

Let's compare Case I's performance with another instrument whose value rose from Rs 10,000 to Rs 20,000 in two years.

Applying the same formula

((20,000/10,000) ^(1/2)) - 1, the CAGR comes to 41.42 per cent.

Hence, if you have to compare the performance of any two asset classes or check returns from an investment over different time frames, CAGR is the best tool as it blocks out all the volatility that can otherwise be confusing.

**8. Loan EMI**

Equated monthly instalments (EMIs) are common in our day-to-day life. At the time of taking a loan, we are shown a neat A4 size paper explaining the EMI structure in a simplified manner. It is generally an unequal combination of principal and interest payments.

We absorb these details and move on with life. But have you ever wondered about the calculation behind these numbers? If you are curious, then here is the formula

**Formula: EMI= (A*R)*(1+R) ^N/ ((1+R) ^N)-1) **

Where A = Loan amount

R = Interest rate N= Duration

Example

Suppose you have taken a loan of Rs 10 lakh at 11 per cent annual interest for 15 years. 1

1 per cent per annum translates into 11/1200 = 0.00916 per month

Tenure = 15*12 = 180 months

EMI = (1000000 x 0.00916) x

((1+.00916) ^180) / ([(1+.00916) ^180] - 1)

= Rs 11,361

This equation helps you check if the bank is charging the right amount.

**9. Future Value of SIP**

We all save small amounts at fixed intervals for a goal. It may be in a mutual fund SIP or PPF. But, how can we know the possible savings ten years down the line? That is where the future value of SIP formula comes into the picture. Let's see how this functions. [ One of the best ways to invest in a mutual fund is SIP. ]

The beauty of the method is that an individual can invest a fixed sum (as low as Rs 500) at regular intervals (monthly, quarterly or half-yearly) in a disciplined manner. It allows one to enjoy the benefits of rupee cost averaging along with compounding. The data required for this calculation are the amount to be invested per month, the rate of return and the period of investment.

**Formula: S = R((1+i)^n-1/i) (1+i) **

Where

S = Future value of investment

R = Regular monthly investment

i = Interest rate assumed /12

n = Duration (number of months or number of years *12)

EXAMPLE

Suppose you are investing Rs 1,000 each month for the next 10 years and expect a return of 15 per cent.

Your return is calculated as follows Payments:

Monthly over next 10 years = 12*10 = 120 months

Interest: 15% per annum - 15/12 = 1.25% = 0.0125

S = 1,000 * [{(1+ 0.0125) ^120 - 1}/0.0125] *

(1+ 0.0125)

The outcome is Rs 2,78,657, which is the future value of the SIP.

So,with this simple formula, you can know the return your investment is likely to generate.

**10. Liquidity Ratio**

Even though it may look like one of the jargons that analysts use to talk about a balance sheet, it is equally important in personal finance.This ratio indicates the overall health of one's finances. It helps see if one is prepared to face a liquidity crunch.

**Formula:Liquidity Ratio = Total liquid assets\Total current debt **

The value of this ratio should ideally be above one.

A less figure indicates that your liabilities are greater than your assets and so your financial stability is under threat.

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