Compound interest and simple interest are the two popular types of interest that come into the picture when talking about any kind of financial instrument, be it stock market investment instruments like mutual funds and shares or loans.
While simple interest is simple and can be calculated easily, compound interest is a bit tricky. However, the deal is that compound interest is highly beneficial for investors as it offers them a chance to maximise their returns over time through the concept of the “power of compounding.”
Most people find the calculation of compound interest challenging. Here is the good news: there are some amazing short tricks and formulas that can help you calculate compound interest quickly, even without using a compound interest calculator.
Whether you are planning to invest or simply want to learn about the easy ways of calculating compound interest, we have got you covered.
In this blog, we will discuss the most useful compound interest tips and tricks.
Keep reading!
What is Compound Interest?
Compound interest is defined as the method of calculating interest levied on a loan or an investment. It is calculated on the principal amount as well as the interest gained on it during the previous cycles. Some people also call it the calculation of interest on gained interest. It is represented by C.I.
Formula for Compound Interest
As mentioned in the above paragraph, compound interest is calculated on the initial amount and the interest accumulated on it previously. Based on it, here is the formula for calculating C.I:
Compound Interest = Amount - Principal
In the above formula, the amount is derived by the below formula:
A = P (1+ r/n)nt
Here,
- A = Total Amount
- P = Initial Principal
- r = Rate of interest on which loan or deposit is disbursed.
- n = number of times the interest is compounded in a year. It can be monthly, half-yearly, quarterly, or yearly.
- t = time in years.
We can also write it as:
C.I = A - P
Or
C.I = P ( 1+ r/n)nt- P
In case the interest is compounded only once per year, the formula becomes:
A = P (1 + R/100)t
Best Compound Interest Tips and Tricks
Now that you have understood the concept of compound interest and the formula for calculating the same, let’s move on to the shortcut to find compound interest:
CompoundInterest Tricks 1:
If a sum of money subject to compound interest becomes x times in ‘a’ years and y times in ‘b’ years, then both of these sums can be related using the below shortcut formula:
(X)1/a= (Y)1/b
Let’s derive this shortcut from the main formula.
A = P (1 + r/100)t
Taking condition 1, the sum becomes x times in ‘a’ year and y times in ‘b’ year. Thus, using the compound interest formula,
xp = p(1 + r/100)a
(X)1/a= (1 + r/100)………………………….(equation I)
In the same way, taking the next condition, the sum becomes y times in ‘b’ year, it becomes:
yp = p(1 + r/100)b
(Y)1/b = (1 + r/100)………………………….(equation II)
On dividing equation I by II, we get:
(X)1/a= (Y)1/b
Let’s now use this trick to solve an example.
Example 1: A sum of money subjected to compound interest becomes 4 times in 4 years. In how many years will it become 16 times itself?
Solution: By using (X)1/a= (Y)1/b
(4)1/4 = (16)1/x
(4)1/4 = (4)2/x
1/4 = 2/x
X = 8
Compound Interest Tricks2:
If an amount grows up to X rupees in T years and Y in (T+1) years subject to compound interest, then the percent of rate can be calculated as:
R% = (Y - X )/ X * 100
Example 2: If an amount of money grows up to ₹5,000 in 4 years and up to ₹7,000 in 7 years, find the rate percent.
Solution: Here,
X = 4
Y = 7
R% = (7- 4) / 4 * 100
R% = 3 / 4 * 100%
R% = 75%
Some Other Important Tips and Formulas for Compound Interest
Following are some other direct formulas you can use to solve various kinds of compound interest problems:
- Always calculate the compound interest on the Amount, i.e. (Principal + Interest).
- Always calculate the simple interest on the Principal.
- If a sum A is compounded annually becomes A1 in t years and A2 in (t+1) years, then the principal can be calculated using:
- P = A1 (A1/A2)t
- In two years, the difference between compound interest and simple interest can be calculated using:
- P x (R)2/ (100)2
- In three years, the difference between compound interest and simple interest can be calculated using:
- [P x (R)2/ (100)2] x [300 + R/ 100]
Final Words
Compound interest is very fruitful for investors as it allows them to make the maximum returns out of their long-term investments. As time passes, the amount gets bigger due to the power of compounding.
However, when it comes to calculating the C.I., things tend to get dicey because of complex and time-consuming formulas and methods.
But say no more!
We have discussed some of the best compound interest tips and tricksusing which you can solve any compound interest problem in minutes.
If you are still struggling with C.I. calculations, try using the Tata AIA compound interest calculator. It will surely help you save a lot of time and effort.
