Calculations to Know

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calculations to know

July 22, 2008

Managing money can involve calculations to understand the worth of an investment. To arrive at a

result, calculations can be done in a different way or by using a different formula.

Even the same formula can be used differently to arrive at a certain result. Here are a few commonly

used money management formulas. Use an excel sheet to do these.

1. Compound Interest

I want to take a loan of Rs 1 lakh to buy a used car. How much will the car cost me at an annual interest

rate of 8 per cent for four years?

The compound interest formula can be used here to calculate the final cost, which would include the

loan amount and the interest paid. The amount that is actually paid for Rs 1 lakh is Rs 1,36,048.90. The

total amount of interest charged for borrowing Rs 1 lakh is Rs 36,048.90.

Formula: Future value = P(1 + R)^N

Type in: =100000(1+8%)^4 and hit enter. P: amount borrowed; R: rate of interest; N: time in years.

Also used for: Calculating the maturity value on lumpsum investment (bank fixed deposits and National

Savings Certificate, for example) over a fixed period at a certain rate of interest.

Text: Sunil Dhawan, Outlook Money

2. Compound Annualised Growth Rate

July 22, 2008

I had invested Rs 1 lakh in a mutual fund five years back at an NAV of Rs 20. Now the NAV is Rs 70.

How should I calculate my returns on an annual basis?

Compound annualised growth rate (CAGR) will be used here to calculate the growth over a period oftime. The gain of Rs 50 over five years on the initial NAV of Rs 20 is a simple return of 250 per cent

(50/20 * 100). However, it should not be construed as 50 per cent average return over five years.

Formula: CAGR = {[(M/I)^(1/N)] 1} * 100

Type in: =(((70/20)^(1/5))-1)*100 and hit enter. M: maturity value; I: initial value; N: time in years. CAGR

here is 28.47%.

Also used for: Calculating the annualised returns on a lumpsum investment in shares.


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10 calculations to know

3. Internal Rate of Return

July 22, 2008

I paid Rs 18,572 every year on a moneyback insurance policy bought 20 years back. Every fifth year, I

received Rs 40,000 back and Rs 4.5 lakh on maturity. What was my rate of return?

The internal rate of return (IRR) has to be calculated here. It is the interest rate accrued on an

investment that has outflows and inflows at the same regular periods.

In the excel page type Rs 18,572 as a negative figure (-18572), as it is an outflow, in the first cell. Paste

the same figure till the twentieth cell.

Then, as every fifth year has an inflow of Rs 40,000, type in Rs 21,428 (40,000-18,572) in every fifth

cell. In the twentieth cell, type in 18572. In the twenty first cell, type in Rs 4,50,000, which is the

maturity value of the policy.

Then click on the cell below it and type: = IRR(A1:A21) and hit enter.

5.28% will show in the cell. This is your internal rate of return.

Also used for: Calculating returns on insurance endowment policies

4. XIRR

July 22, 2008

I bought 500 shares on 1 January 2007 at Rs 220, 100 shares on 10 January at Rs 185 and 50 shares

at Rs 165 on 18 May 2008. On 21 June 2008, I sold off all the 650 shares at Rs 655. What is the return

on my investment?

XIRR is used to determine the IRR when the outflows and inflows are at different periods. Calculation is

similar to IRR's. Transaction date is mentioned on the left of the transaction.

In an excel sheet type out the data from the top most cell as shown here. Outflows figures are in

negative and inflows in positive. In the cell below with the figure 4,25,750, type out

=XIRR (B1:B4,A1:A4)*100

Hit enter. The cell will show 122.95%, the total return on investment.

Also used for: Calculating MF returns, especially SIP, or that for unit-linked insurance plans.


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7. Inflation

July 22, 2008

My family's monthly expense is Rs 50,000. At an inflation rate of 5 per cent, how much will I need 20

years hence with the same expenses?

The required amount can be calculated using the standard future value formula. Inflation means that

over a period of time, you need more money to fund the same expense.

Formula: Required amt.=Present amt. *(1+inflation) ^no. of years

Type in: =50000*(1+5% or .05)^20 and hit enter. You will get Rs 1,32,664 as the answer, which is the

required amount.

Also used for: Calculating maturity value on an investment.

. Purchasing Power

July 22, 2008

My family's monthly expense is Rs 50,000. At an inflation rate of 5 per cent, how much will be the

purchasing value of that amount after 20 years?

Inflation increases the amount you need to spend to fetch the same article and in a way reduces the

purchasing power of the rupee. Here, Rs 50,000 after 20 years at an inflation of 5 per cent will be able

to buy goods worth Rs 18,844 only.

Formula: Reduced amt.= Present amt. / (1 + inflation) ^no. of yrs

Type in: =50000/(1+5%)^20 and hit enter. You will get Rs 18,844, which is the reduced amount

9. Real Rate of Return

July 22, 2008

My father wants to make a one-year bank FD at 9 per cent. On maturity, he says, the capital will be

preserved and he would get assured return on it.

It is true that fixed deposit is safe and gives assured returns. However, after adjusting for inflation, the

real rate of return can be negative.

Formula: Real rate of return=[(1+ROR)/(1+i)-1]*100


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Type in: =((1+9%)/(1+11%)-1)*100 and hit enter. -1.8% is the real rate of return. ROR: Rate of return

per annum; i: rate of inflation (11 per cent here).


10. Doubling, Tripling of Money

July 22, 2008

I can get 12 per cent return on my equity investments. In how many years can I double or even triple my

money?

Formula: No. of years to double = 72/expected return

Type in: =72/12 and hit enter. You will get 6 years. For tripling, type in: =114/12 and hit enter. You will

get 9.5 years. For quadrupling, type in: =144/12 and hit enter to get 12 years.

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