## 10 Calculations To Know.... (MUST READ)

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 lump sum investment (bank fixed deposits and National Savings Certificate, for example) over a fixed period at a certain rate of interest.

2. Compound Annualized Growth Rate

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 annualized growth rate (CAGR) will be used here to calculate the growth over a period of time. 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 annualized returns on a lump sum investment in shares.

3. Internal Rate of Return

Ipaid Rs 18,572 every year on a money back 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

Ibought 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.

5. Post-Tax Return

My father wants a bank FD at 10 per cent return for five years. He pays income tax. What will be the returns?

The post-tax return has to be calculated here. The idea is to know the final returns on a fully taxable income. Interest income from the bank is taxed as per your tax slab.

Formula: ROI ? (ROI * TR)=Post-tax return

Type in: =10 ? (10 * 30.9%) and hit enter. You will get 6.91%

ROI: rate of interest; TR: tax rate (depends on tax slab)

Also used for: Calculating post-tax returns of national savings certificates, post-office time deposits, and Senior Citizens' Savings Scheme.

6. Pre-Tax Yield

My brother says that the investment in public provident fund (PPF), which gives 8 per cent, is the best. Isn't 8 per cent a low rate of return?

An investment's pre-tax yield tells us if its return is high or low. The return on PPF (8 per cent) is tax-free. Also, this has to compared with returns of a taxable income to estimate its worth. For someone paying a tax of 30.9 per cent, the pre-tax yield in PPF is 11.57 per cent. At present, there is no fixed, safe and assured-return option that has 11.57 per cent return and a post-tax return comparable to PPF's 8 per cent.

Formula: Pre-tax yield = ROI / (100-TR)*100

Type in: =8/(100-30.9)*100 and hit enter. You will get 11.57%. ROI: rate of interest, TR: tax rate, (depends on tax slab)

Also used for: Calculating the yield on an Employees' Provident Fund or any other tax-free instrument.

7. Inflation

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.

8. Purchasing Power

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

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

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

Ican 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