Personal Finance Math (Part 1)
Simple Interest
When it comes to personal finance, one of the key things to learn is the math that surrounds this topic.
In this chapter, we will learn the most basic math involved starting from simple interest.
Imagine that one of your friends needs money urgently and he approaches you for it. Being a friend, you agree to help him with the money but you also expect your friend to pay you ‘interest’ on the cash you lend to him.
The transaction details are below –
Amount – BDT 100,000/-
Tenure – 5 years
Interest (%) – 10
As you can see, your friend agrees to repay BDT n100,000/- over a 5 year period 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, the yearly interest is paid on the principal amount.
Principal = BDT 100,000/-
Interest = 10%
Yearly interest amount = 10% * 100,000
= BDT 10,000/-
Here is how the math looks –
|
Year
|
Principal outstanding
|
Interest payable
|
|
01
|
BDT 100,000
|
BDT 10,000
|
|
01
|
BDT 100,000
|
BDT 10,000
|
|
03
|
BDT 100,000
|
BDT 10,000
|
|
04
|
BDT 100,000
|
BDT 10,000
|
|
05
|
BDT 100,000
|
BDT 10,000
|
Total Interest received BDT 50,000/-
So as you can see, you can earn BDT 50,000/- in total interest from this payment. The amount you earn from the interest can also be calculated by applying a simple formula, which you may remember from your school days –
Amount = Principal * Time * Return
Where the return is the interest percentage.
Amount = BDT 100,000 * 5 * 10%
= BDT 50,000/-
In simple interest, the interest gets charged only on the outstanding principal.
Imagine a bank transaction, you deposit BDT 100,000/- in a bank’s Fixed Deposit scheme, which promises to pay you a simple interest of 10% year on year for 5 years. At the end of 5 years, you’ll earn BDT 50,000/- as interest income.
Banks don’t pay simple interest, they pay compound interest. What do you think is the difference between simple interest and compound interest?
Compound interest
Compound interest works differently compared to simple interest. If someone agrees to pay you compound interest, then it essentially means that the person or the entity is agreeing to pay you interest on the interest already earned.
Let’s figure this out with the same example discussed above. The transaction details are as follows –
Amount – BDT 100,000/-
Tenure – 5 years
Interest (%) – 10
Interest type – Compound Interest (compounded annually)
The math is as follows –
Year 1
At the end of 1st year, you are entitled to receive a 10% interest on the principal outstanding and previous interest (if any). For a moment assume you are closing this at the end of the 1st years, then you would receive 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 obviously the principal. Applying this –
= 100,000 *(1+10%)
= 110,000
Year 2
Now assume, you want to c lose this in the 2nd year instead of the first, here is how much you’d g et back –
Remember, you are supposed to get paid interest on the interest earned in the first year, hence –
Principal *(1+ Interest) * (1+Interest)
The green bit is the amount receivable at the end of 1st year, and the blue bit is the interest applicable for the 2nd year.
We can simplify the above equation –
= Principal*(1+ Interest)^(2)
= 100,000*(1+10%)^(2)
= 121,000
Compounded returns
The concept of compounded return is similar to compound interest. The interest is what you pay when you borrow money in any form and the return is what you earn when you invest your money in any asset. If your investment horizon is more than a year, you will use CAGR or the compounded annual growth rate, to measure returns.
The difference between absolute and CAGR is best understood with an example.
Assume you invested BDT 100,000/- on 1st Jan 2019 in a financial instrument which yields you a 10% return (per year) and you withdraw this investment a year later. How much money do you make?
Quite straight forward as you can imagine –
You will make 10% of 100,000 which is BDT 10,000/-, in other words, your investment has grown by 10% on a year on year basis. This is the absolute return. This is straightforward because the time under consideration 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 o f a simple return of 10%, the return was compounded annually at 10%? How much money would you make a t the end of 3 years?
To calculate this, we s imply have to apply the growth rate formula –
Amount = Principal*(1+return)^(time)
Which as you realize is the same formula used while calculating the compound interest. Applying this formula –
=100,000*(1+10%)^(3)
= BDT 133,100/-
Referring to the previous section, if you were to charge compound interest, then this is the same amount of interest you receive from y our friend in the 3rd year.
Continuing on the same lines, here is another question –
If you invest BDT 100,000/- and receive BDT133,100/- after 3 years, then what is the growth rate 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 so, the formula reworks itself to –
Return = [(Amount/Principal)^(1/time)] – 1
Return here is the growth rate or the CAGR.
Applying this to the problem –
CAGR = [(133100/100000)^(1/3)]-1
= 10%
