When it comes to personal finance, one of the important things to learn is the math that surrounds the subject. Once you understand a bit of math, the rest is just use and life becomes easier after that.

In this article, I will try to explain and explain the most basic of mathematics, starting with simple interest. I know this is explained in several chapters in several modules at the varsity, but for the sake of completeness let me cover it in a single chapter.

Let us walk through a hypothetical transaction, which I guess is a familiar situation to most of us.

Imagine that a friend of yours is in urgent need of money and he approaches you for it. Being a friend, you agree to help him with money, but being a capitalist at heart, you also expect that your friend will pay you ‘interest’ on the cash you lend him . I know we don’t usually ask a friend to pay us interest, but let’s say it’s a friend you want to help, but not at the opportunity cost of your money.

The transaction details are given below –

- Amount – 100,000/-
- Tenure – 5 years
- Interest (%) – 10

As you can see, your friend agrees to repay Rs.100,000/- over a period of 5 years and also agrees to pay you an interest of 10%.

Given this, how much money will you make at the end of 5 years? Let’s do the math and find out the details.

Remember, annual interest is paid on the principal amount.

**Principal = 100,000/-**

**interest = 10%**

**Annual interest amount = 10% * 100,000**

**= Rs.10,000/-**

Here’s what the math looks like –

year |
principal arrears |
interest payable |
---|---|---|

01 | Rs.100,000/- | Rs.10,000/- |

02 | Rs.100,000/- | Rs.10,000/- |

03 | Rs.100,000/- | Rs.10,000/- |

04 | Rs.100,000/- | Rs.10,000/- |

05 | Rs.100,000/- | Rs.10,000/- |

total interest received |
Rs.50,000/- |

So as you can see, you will get Rs. 50,000/- can earn. The amount to be earned from interest can also be calculated by applying a simple formula which you may remember from your school days –

**Amount = Principal * Time * Return **

where return is the interest percentage.

Amount = Rs.100,000 * 5 * 10%

, **Rs.50,000/-**

I am sure you will agree that it is quite straightforward and most of you will remember that it is simple interest.

In simple interest, interest is charged only on the outstanding principal.

Imagine a bank transaction, you deposit Rs.100,000/- in a fixed deposit scheme of a bank, which promises to pay you 10% simple interest annually for 5 years. At the end of 5 years, you can earn Rs. 50,000/- will earn. The math is still the same.

Banks do not give simple interest, they give compound interest. What do you think is the difference between simple interest and compound interest?

**Compound Interest**

Compound interest works differently than simple interest. If someone agrees to pay you compound interest, it essentially means that that person or entity is agreeing to pay you interest on the interest already earned.

Let us understand it with the same example discussed above. The transaction details are as follows –

- Amount – 100,000/-
- Tenure – 5 years
- Interest (%) – 10
- Type of interest – Compound interest (compounded annually)

The math is as follows-

**year 1**

1. At the end of^{scheduled tribe} year, you are entitled to receive 10% interest on the principal outstanding and past interest (if any). Let’s assume for a moment that you call it 1. closing at the end of^{scheduled tribe} year, then you will get the principal amount plus the interest applicable on the principal amount.

Amount = Principal + (Principal * Interest), this can be simplified to

= principal * (1+ interest)

Here, (1+interest) is the ‘interest’ part and the principal is clearly the principal. apply it –

= 100,000 *(1+10%)

= 110,000

**year 2**

Now suppose you call it 2. I want to close^{Ra} Instead of years ago, here’s how much you’ll get back –

Remember, you should get the interest paid on the interest earned in the first year, so –

Principal *(1+interest) *(1+interest)

green bit 1. The amount receivable at the end of^{scheduled tribe} year, and blue bit 2. interest is applicable for^{Ra} year.

We can simplify the above equation to –

= principal *(1+ interest)^(2)

= 100,000*(1+10%)^(2)

= 121,000

**season 3**

3. In^{third} year, you 1. will get interest on^{scheduled tribe} interest for two years. mathematics –

Principal *(1+interest) *(1+interest) *(1+interest)

The green bit is the amount receivable at the end of 2 years, and the blue bit is the applicable interest for 3 years.^{third} year.

We can simplify the above equation to –

= principal *(1+ interest)^(3)

= 100,000*(1+10%)^(3)

= 133,100

We can generalize this –

**p*(1+r)^(n)**where –

- P = Principal
- R = interest rate
- n = tenure

So, if you open it for full 5 years, you will get –

= 100,000*(1+10%)^(5)

,**Rs.161,051/-**

Compare the difference between 50K received in simple interest vs. 61,051/- received by way of compound interest.

Compound interest and compound return work magic in finance. At the end of the day, every aspect of personal finance boils down to compounding returns. For this reason, I think it’s best to spend some more time trying to understand the concept of compounding money.

**compound return**

The concept of compound interest is similar to that of compound interest. The concepts of return and interest are very similar like two sides of the same coin. Interest is what you pay on borrowing in any form and return is what you earn on investing in an asset. So if you understand interest then it is easy to understand returns.

In this section, you will learn how returns are measured. Depending on the timing of your investment, the return measurement varies.

you will use **Pure **Method to measure returns if your investment horizon is less than one year. Otherwise, if your investment horizon is more than one year, you will use the CAGR or **compound annual growth rate**To measure returns.

I think the difference between absolute and CAGR is best understood with an example.

Let’s say you have 1. Has invested Rs.100,000/- on^{scheduled tribe} January 2019 in a financial instrument which gives you 10% return (per annum) and you withdraw this investment after one year. how much money do you make?

Pretty straight forward as you can imagine –

You will earn 10% of 100,000 which is 10,000/-, in other words, your investment has grown by 10% on a yearly basis. This is a full refund. This is straightforward because the time in question is 1 year or 365 days.

Now, what if the same investment was held for 3 years instead of 1 year, and what if instead of a simple return of 10%, the returns compounded annually at 10%? How much money will you make at the end of 3 years?

To calculate this, we just need to apply the growth rate formula –

**Amount = Principal*(1+Return)^(Time)**

As you realize the same formula is used while calculating compound interest. Applying this formula –

100,000*(1+10%)^(3)

, **Rs.133,100/-**

Referring to the previous section, if you were to charge compound interest, this is the same amount that you would have received from your friend in 3^{third} year.

Continuing along the same lines, here is another question –

If you invest 100,000/- and get 133,100/- after 3 years, what is the rate of growth of your investment?

To answer this question, we just need to reorganize this formula –

**Amount = Principal*(1+Return)^(Time)**

and solve for ‘return’.

By doing this, the formula reworks itself –

**return** , **[(Amount/Principal)^(1/time)] – 1**

Here the return is the growth rate or CAGR.

Applying it to the problem –

CAGR = [(133100/100000)^(1/3)]-1

, **10%**

**compound effect**

Obviously, Albert Einstein once defined ‘compound interest’ as 8. was described as^{th} wonder of the world. I guess he couldn’t describe it better. To understand why you need to understand compound interest over time.

Compounding in the finance world refers to the ability of money to grow, given that year 1 gains are reinvested for year 2, year 2 gains are reinvested for year 3, and so on. Too.

For example, let’s say you invest Rs 100 which is expected to grow by 20% year on year (remember this is also called CAGR or simply growth rate). At the end of the first year, the money increases to Rs 120.

At the end of year 1, you have two options –

- Suppose a profit of Rs 20 is invested with a principal principal of Rs 100 or
- Withdraw profit of Rs 20

You decide not to withdraw profit of Rs.20; Instead, you 2. decide to reinvest the money for^{Ra} year. 2 . At the end of^{Ra} year, 120 Rs. 20% @ Rs. becomes 144. 3. At the end of^{third} Year, Rs 144 increased by 20% to Rs 173. So on and so forth.

Compare this with the withdrawal of profit of Rs 20 every year. If you had opted to withdraw Rs 20 every year then 3. At the end of^{third} The profit accumulated for the year will be Rs. 60.

However, since you have decided to stay invested, the profit at the end of 3 years is Rs 173/-. This is Rs 13 over Rs 60 or 21.7% as good because you chose to do nothing and decided to stay invested.

it is called **compound effect**,

Let’s take this analysis a bit further, take a look at the chart below:

The chart above shows how Rs 100 invested grows at the rate of 20% over a period of 100 years.

In the next chapter, we will understand the other important concept in personal finance – the time value of money.

**Highlights of this chapter**

- Simple interest is the interest that is paid only on the outstanding principal
- Compound interest is paid on both the interest and the principal
- Interest and consideration are two sides of the same coin
- Absolute return is a measure of the increase in return when your investment is held for less than a year
- Compounded Annual Growth Rate (CAGR) is a measure of your return when your investment tenure is more than one year
- Compounding works best when you give your investment enough time to grow