  # Compound Interest and Simple Interest Understanding Personal Finance Maths

Simple Interest

Understanding the maths behind personal finance is essential for mastering the subject. Once you have a handle on this idea, it will become increasingly easy to move forward with your financial knowledge.

This chapter aims to cover the most basic mathematics involved, particularly focusing on simple interests.

Let us take a look at an imaginary transaction:

Suppose a friend of yours is in need of money desperately and comes to you for assistance. Thinking of them as a friend, you are willing to give them the financial aid they require; nonetheless, being capitalists at heart, you furthermore expect compensation, or interest, on the sum you lend. It may sound strange to ask a buddy for remuneration; however, consider that it’s still valued assistance from your side – with no expense to your capital.

The transaction details are below:

Amount – Rs.100,000/-

Tenure – 5 years

Interest (%) – 10

As it is evident, your buddy has agreed to reimburse Rs.100,000/- over a 5-year period and pay you an interest rate of 10%.

How much money will you have accumulated after 5 years? Let’s look into the specifics by doing the math.

Don’t forget the annual interest rate is applicable to the original sum.

The total amount of money being invested is Rs.100,000. This sum represents the principal value.

The interest rate is 10%

Yearly interest amount = 10% * 100,000

= Rs.10,000/-

This is the maths:

By applying the formula, you can obtain a total of Rs.50,000/- in interest.

Amount = Principal * Time * Return

Where the return is the interest percentage.

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

= Rs.50,000/-

In the case of simple interest, only the outstanding amount of the principal is used to calculate interest.

Imagine a bank deposit. You put Rs.100,000/- in a Fixed Deposit, with an annual interest rate of 10%, for a term of 5 years. The resultant interest earned will be Rs.50,000/-. The calculations remain unchanged.

Banks don’t offer simple interest, they provide compound interest. Can you spot the difference between the two?

Compound interest

Compound interest is different from simple interest: the person or entity agreeing to pay compound interest is essentially being asked to add the sum of past interest rates onto the principal amount.

We can look at the same example mentioned earlier and see that the transaction details are as follows –

Amount – Rs.100,000/-

Tenure – 5 years

Interest (%) – 10

Interest type – Compound Interest (compounded annually)

Here’s the maths:

Year 1

At the end of your first year, you are entitled to 10% interest on the principal balance, including any prior interest. If you chose to finish at this point, you would get the starting capital with the interest applicable accruing to it.

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

= Principal * (1+ interest)

Here, (1 + interest) represents the interest portion; the principal is the original amount. With this in mind –

= 100,000 *(1+10%)

= 110,000

Year 2

Take a look at what would happen if you decided to close this in the second year, instead of the first; here’s how much you’d get back.

You should receive not only the interest earned in the first year, but additional earnings from interest on that amount.

Principal *(1+ Interest) * (1+Interest)

Let’s simplify it further:

= Principal *(1+ Interest)^(2)

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

= 121,000

Year 3

In the 3rd year, interest from the first two years would be included in the overall earnings. Let’s do some math:

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

The green section is the total receivable after two years, and the blue is the interest for year three.

We can make the above equation simpler.

= Principal *(1+ Interest)^(3)

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

= 133,100

This principle can be applied anywhere.

P*(1+R)^(n), where –

P = Principal

R = Interest rate

N = Tenure

So, if you were to have this open for the entire 5 years, you’d receive –

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

=Rs.161,051/-

Compare the amount of Rs.50,000 earned from simple interest to the sum of Rs.61,051 gained from compound interest.

Compound interest and compounded return are powerful tools when it comes to managing your finances. Ultimately, all aspects of personal finance can be reduced to a single concept: compounding of money. It is worth investing extra time in comprehending this concept.