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Understanding the concept of compound interest, its formula, and how it is calculated is useful because it is the basis of how interest is calculated for your stock market investments, fixed deposits, recurring deposits, etc. It can help you determine how much your return on investment will be, thereby helping you to plan your savings even better. Retail loans such as home loans and vehicle loans also use the compound interest formula so understanding this will give you a better picture of how much interest you will be paying over the years. Here's an example of how it grows year by year:
There are generally two types of compound interest used.
There are two formulas you can use to calculate compound interest, depending on what result you wish to find out. You can find out the following:
Formulas can be a deterrent to many. If you aren’t savvy with math, your eyes turn away from these codes or just skip them altogether. But once it’s explained, it’s pretty simple to understand. To calculate the total value of your deposit, the formula is as follows:
P (1+ i/n)^{nt}
P = Principal invested.
i = Nominal Rate of Interest.
n = Compounding Frequency or number of compounding periods in a year.
t = Time, meaning the length of time the interest is applicable, generally in years.
Simply put, you calculate the interest rate divided by the number of times in a year the compound interest is generated. For instance, if your bank compounds interest quarterly, there are 4 quarters in a year, so n = 4. This result must be multiplied to the power of the deposit period. For example, if your deposit is for 10 years, t = 10. This whole result should be multiplied by the principal you invested. The result generated will equal the total accumulated value of your deposit. You can find out how much your deposit is worth currently after accumulating interest.
To find out how much interest was earned, you can use the following formula for Compound Interest
P[(1+ i/n))^{nt}-1]
To understand the compound interest equation further, we can break it down in simpler terms. If you decide to invest in a fixed deposit with compound interest, this is how you will earn interest every year.
Period | Deposit Balance |
---|---|
Investment | P |
Year 1 | P + iP |
Year 2 | (P+ iP) + i(P+iP) |
To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:
Period | Deposit Balance |
---|---|
Investment | P |
Year 1 | P(1+i) |
Year 2 | P(1+i)^{2} |
Year 3 | P(1+i)^{3} |
To calculate the compound interest for a number of years together, we need to multiply P(1+i) to the power of the number of years of the deposit. So we end up with this formula:
P (1+ i/n)^{n}
This formula can be used to calculate compound interest that is compounded annually. This means you receive interest only once a year. It is added to your principal, and you continue to earn interest on the new amount.
If you are earning interest multiple times in a year, you need to factor in this number into the equation. So the formula generated is:
P (1+ i/n)^{nt}
This formula can also be used for instances where the interest is compounded once every two years. In this case, n = 0.5, as each year is calculated as half.
For example, Rs. 10,000 is invested in a fixed deposit for 10 years. The interest is compounded every quarter which means 4 times in a year. The interest paid by the bank is 5%. To find out your nominal rate of interest, you need to divide 5 by 100 which equals 0.05. Now, we look at the formula and substitute the letters with the relevant numbers.
P (1+ i/n)^{nt}
Step 1: 10,000 (1+0.05/4)^{4x10}
Step 2: 10,000(1+0.0125)^{40}
Step 3: 10,000 (1.0125)^{40}
Step 4: 10,000 (1.64361946349)
Step 5: 16436.1946349
We can round of this total to Rs. 16,436.19. So the compound interest earned after 10 years is Rs. 6,436.19.
We can also arrive at this figure using the formula for compound interest earned. We can substitute the numbers for letters as seen below:
P[(1+ i/n)^{nt } -1]
Step 1: 10,000 [(1+0.05/4)^{4x10} -1]
Step 2: 10,000 [(1+0.0125)^{40}-1]
Step 3: 10,000 [(1.0125)^{40}-1]
Step 4: 10,000 [(1.64361946349) -1]
Step 5: 10,000 (0.664361946349
Step 5: 6436.1946349
We can now add this interest earned to the principal amount to find out the value of the deposit. The maturity value will be Rs. 16,436.19.
The earnings through compound interest can be demonstrated with the following graph.
To demonstrate the difference between simple interest and compound interest, let’s take for example two fixed deposits. Both deposits are of Rs. 10,000 for 10 years. The interest offered on Deposit 1 is 5% compound interest. The interest offered on Deposit 2 is 5% simple interest. The interest is calculated annually on both deposits.
Period | Deposit 1 - Compound Interest | Deposit 2 - Simple Interest | Difference |
---|---|---|---|
Year 1 | Rs. 500 | Rs. 500 | Rs. 0 |
Year 2 | Rs. 1,025.00 | Rs. 1,000 | Rs. 25 |
Year 3 | Rs. 1,576.25 | Rs. 1,500 | Rs. 76.25 |
Year 4 | Rs. 2,115.06 | Rs. 2,000 | Rs. 115.06 |
Year 5 | Rs. 2,762.82 | Rs. 2,500 | Rs. 762.82 |
Year 6 | Rs. 3,400.96 | Rs. 3,000 | Rs. 400.96 |
Year 7 | Rs. 4,071.00 | Rs. 3,500 | Rs. 571.00 |
Year 8 | Rs. 4,774.55 | Rs. 4,000 | Rs. 774.55 |
Year 9 | Rs. 5,513.28 | Rs. 4,500 | Rs. 1,013.28 |
Year 10 | Rs. 6,288.95 | Rs. 5,000 | Rs. 1,288.95 |
From the graph above, we can see clearly the higher earnings through compound interest compared to simple interest. The difference is not too much upto the 4th year. This is because the interest accumulated over the years is added to the principal, thus making the principal significantly higher. From Year 5, there is a major difference in the interest earned. At the end of 10 years, Deposit 1 earns Rs. 6,288.95, while Deposit 2 earns Rs. 5,000. The difference between the two is Rs. 1,288.95.
Compounding interest on fixed deposits where you are allowed to make monthly contributions can get a little tricky. For the amount invested during the compounding period, interest will be generated for the initial investment amount + monthly contributions. These deposits are rare but are an extremely good investment with whopping returns.
For example, Rs. 10,000 is the initial fixed deposit amount. The investor deposits Rs. 1,000 every month for 5 years. If the interest is compounded annually, then the interest will be as follows:
Period | Investment Breakdown | Investment + Interest Accumulated | Interest Earned | Total Value of Deposit |
---|---|---|---|---|
Year 1 | 10,000 + 12,000 | 22,000 | 1,100 | 23,100 |
Year 2 | 10000 + (12000 x 2) + 1,100 | 35,100 | 1,755 | 36,855 |
Year 3 | 10000 + (12000 x 3) + (1,100 +1,755) | 48,855 | 2,442.75 | 51,297.75 |
Year 4 | 10000 + (12000 x 4) + (1,100 +1,755 + 2,442.75 ) | 63.297.75 | 3164.87 | 66,462.64 |
Year 5 | 10000 + (12000 x 5) + (1,100 +1,755 + 2,442.75 + 3164.87 ) | 78,461.75 | 3,923.13 | 82,385.77 |
Through this table, we can see that the interest earned is accumulated every year and added to the principal amount. The total money contributed by the investor is Rs. 10,000 initially, followed by Rs. 1,000 every month or Rs. 12,000 every year. The investor made a total contribution of Rs. 10,000 + Rs. 60,000. At the end of 5 years, the value of his deposit is Rs. 82,385.77. The total compound interest earned is Rs. 12,385.77.
Compound interest is your biggest friend when it comes to deposits and investments. Working in favor of investments, you stand to gain much more from the interest payable. But compound interest will be your worst enemy when it is calculated on your loan or other debt. You will end up paying significantly more interest on your loan. In terms of fixed deposits, compound interest is a great way of earning more on your investment. You earn much higher returns with compound interest on long term deposits. Compounding interest monthly, quarterly and half-yearly can spike your interest even higher. The benefits of compound interest can be listed as follows:
Compound interest is used for both debit and credit aspects of the financial world. Listed below are some of the investments and credit options that use compound interest.
Investments
Debt
When it is used in case of deposits and investments, we stand to benefit. On the other hand, when compound interest is charged on loans and debt, the banks and lenders stand to gain.
Your investments will grow faster if it is calculated on the compound interest method as compared to the simple interest method because simple interest is calculated only on the principal amount whereas compound interest is calculated both on the principal and interest amount every year.
The schedule for compounding interest used by savings bank accounts is on a daily basis.
Compounding interest is more beneficial to an investor than for a borrower.
ICICI Bank on Tuesday raised the interest rates on deposits over Rs. one crore in the range between 5 and 35 basis points. The rates of bulk deposits which matures in the range of 30 days to 45 days were raised by the bank to 5.75 percent.The interest rates for those bulk deposits that matures between 46 days and 60 days as well as for those maturing between 61 days and 90 days were raised to 6.25 percent each. While the rates for deposits that matures between 91 days and 184 days was raised of 35 basis points, which means that the interest rate would now be 6.65 percent. That will also be the interest rates for deposits that matures in the period of 185 days to 364 days. The interest rates on bulk deposits maturing in the period between one year to 389 days saw a raise of 5 basis points and went up 6.75 percent. The rates on deposits of longer maturities however remained unchanged at 6.5 percent.
The increase in the interest rates by ICICI bank comes after State Bank of India (SBI), Punjab National Bank (PNB) and Bank of Baroda (BoB) did so in the recent past.
10th January 2018
A Fixed Deposit (FD) is a safe investment option that offers guaranteed returns and also comes with tax benefits.
Tax saving term deposits come with a lock-in period of 5 years and you can claim deduction of up to Rs.1.5 lakh under section 80C of the Income Tax Act.
Now, let us take a look at the FD interest rates of top banks. SBI, for example, offers an interest rate of 6.25% for general FDs and 6.75% for senior citizen term deposits. ICICI Bank offers 6.6%, HDFC pays 6.75%, while Kotak Mahindra pays 6.75% for all time deposits held for 1 year.
24th December 2017
The government is likely to think of lower tax rates and this is because the current rates and slabs are more open than the ones that were decided earlier code. The previous direct tax code was composed by the committee constituted by the United progressive Alliance government.
According to officials, the main objective is to encourage Indians to pay tax and keep the direct tax and GDP ratio near the 18% figure.
4 December 2017
After revising fixed deposit rates, HDFC has also slashed MCLR rate, expanded as the Marginal Cost of Lending. The rate was reduced by 5 basis points.
According to a representative from the bank, the MCLR rate for one year tenure is 8.1% and the rate for 6 months is 7.9%. These changes will be effective from November 7, 2017. This rate reduction will be applicable for all tenures.
9 November 2017
The Reserve Bank of India (RBI) has set the reference rate for the rupee at 64.8064. This rate has been set against the US dollar.
The reference rate against the Euro for the Indian rupee is 75.2273. For the pound, the rate is 85.3371 and for the yen the rate set is 56.85 per 100 yen.
This rate has been decided after comparing dollar rates and other cross currency quotes.
The Special Drawing Rates for Indian currency will be determined based on this reference rate set by the RBI.
7 November 2017
Tax rates are likely to be slashed on certain common use items such as shampoo, soap, plastic products, handmade furniture and the like. The Goods and Services Tax (GST) Council is mulling over considering slashing the 28% GST on various items.
A decision is likely to be made to benefit both business and consumers with regard to products that fall under the 28% tax bracket. There are many plastic goods that fall under the 18% bracket, while other products fall under the 28% tax bracket.
The GST Council has rationalised rates for as many as 100 items in the recent past.
5 November 2017
The State Bank of India (SBI) is now offering cheaper loans in the home and auto sector. This move is part of the rate revision strategy and the same is likely to be implemented by other banks in the near future.
The bank claims that this is the lowest rates offered in the industry. At present home loans are being offered at the rate of 8.3%, compared to the earlier 8.35%. On the car loan front, the interest rate has been reduced to 8.7% from 8.75%.
SBI has also slashed the interest rate offered on fixed deposits.
3 November 2017
Many small finance banks that were luring customers with a high interest rate that went up to over 9%, are now under pressure to cut down their interest rates on term deposits.
It is important to note here that though these banks may cut down their interest rates, the rate of return offered will still be much higher when compared to other banks in the industry. The rate of interest offered by these banks is around 50 to 100 basis points higher than industry rates.
Some of the small finance banks include Suryoday, ESAF, Fincare Small Finance, Capital Local Area Bank, etc. Suryoday Small Finance Bank was offering an interest rate of 8.75% for deposits held for 2 years to 3 years.
2 November 2017
There is still a cloud of confusion whether Repo rate will be changed in December, this year. A member of the Monetary Policy Committee (MPC) has urged that the Reserve Bank of India (RBI) to be mentally prepared to deal with the various drivers of inflation in the Indian economy.
There has been talks about pushing the manufacturing sector. The fall in the growth of investments could be because of the slump in household investment in dwellings.
If inflation touches us, it could lead to a lot of dangers. This may be likely due to the fall in fiscal deficit.
23 October 2017
The Jharkhand government will be guaranteeing the education loans of students from SC/ST and OBC categories from the following academic year.
Eligible students who apply for an education loan will be guaranteed by the government for a sum of over Rs.7.5 lakh, thus enabling them to pursue higher education. The guarantee will be provided under the Jharkhand Education Loan Guarantee Scheme, which can be accessed online.
Courses at all state and central universities as well as NIT, AIIMS and IIT’s will be eligible for the education loans.
27 March 2017
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