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  • Gone are the days of school mathematics, most of us easily forget, but a quick refresher may bring it all back. To understand compound interest in the easiest form, let’s take a look at what it means. Compound interest is a useful financial concept in which your interest earned is added to your principal. This amount then continues to earn more interest. So in this case, you also earn interest on the interest you’ve already earned. So your balance grows at an increasing rate. In a sense, you reinvest your interest, rather than receiving a pay-out.

    • Year 1 - You earn interest on your Principal.
    • Year 2 - You earn interest on your (Principal + Interest of Year 1).
    • Year 3 - You earn interest on your (Principal + Interest of Year 1 + Interest of Year 2).

    Compound interest is the basis of long-term growth of the stock market. It forms the basis of personal savings plans. Compound interest also affects inflation.

    Types of Compound Interest

    There are generally two types of compound interest used.

    • Periodic Compounding - Under this method, the interest rate is applied at intervals and generated. This interest is added to the principal. Periods here would mean annually, bi-annually, monthly, or weekly.
    • Continuous Compounding - This method uses a natural log-based formula and calculates interest at the smallest possible interval. This interest is added back to the principal. This can be equalled to the constant rate of growth for all natural growth. This figure was born out of physics. It uses Euler’s number which is a famous irrational number which is known to more than 1 trillion digits of accuracy. Euler’s number is denominated by the letter “E”.

    Periodic Compound Interest Formula Overview

    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:

    • The total value of the deposit.
    • The total compound interest earned.

    Value of the Deposit

    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.

    Total Compound Interest Earned

    To find out how much interest was earned, you can use the following formula for Compound Interest.

    P[(1+ i/n))nt-1]

    Compound Interest Equation and Calculation

    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

    Formula for Annual Compound Interest

    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.

    Half-Yearly, Quarterly, Monthly Compound Interest Formula

    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.

    Examples of Compound Interest

    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.

    Calculating the Total Value of the Deposit

    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.

    Calculating the Interest Earned

    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.

    FD Compund Interest

    Simple Interest vs. Compound Interest

    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
    FD Comparison

    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.

    Compound Interest with Monthly Contributions

    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.

    The Benefit of Compound Interest

    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:

    • Reinvestment - The interest earned will be reinvested into the same deposit.
    • Higher value of the deposit - Compound interest leads to a higher value of the deposit. Upon maturity, your deposit will be more than a deposit with simple interest.
    • Long-term savings - Compound interest deposits encourage long-term savings as the return on investment is much higher after 10 years or more.
    • Increased Earnings - Options of compounding monthly, quarterly, and half-yearly increase the interest earned.

    Financial platforms where compound interest is applicable

    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

    • Savings Accounts
    • Fixed Deposits
    • Recurring Deposits
    • Other Certificates of Deposits
    • Reinvested Dividend Stocks
    • Retirement Funds

    Debt

    • Loans
    • Credit Cards
    • Mortgages

    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.

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    Compound Interest Formula Reviews

    • ICICI Bank Fixed Deposit
      "Good investment for future"
      0.5 4.0/5 "Great!"
      I opened fixed deposit with ICICI it gives tax benefits upto 80 c section, I invest Rs. 50,000 as a one time investment it has the term of five years. The online banking is good to deposit the money to take the liquidity, I have option to track the FD details also netbanking.
      Was this review helpful? 0
      , bangalore
      Reviewed on Jul 19, 2019
    • Union Bank of India
      Union Bank of India Fixed Deposit
      "Its Recommendable "
      0.5 5.0/5 "Blown Away!"
      I have fixed deposit with Union Bank of India, I opt for one year fixed deposit , they are providing 8.60% of interest for per annum. I got the profit around Rs. 8000 for the amount invested amount of around Rs. 1.60 lakh, I would recommend this service. They do have option to deposit the amount through online.
      Was this review helpful? 0
      , hyderabad
      Reviewed on Jul 18, 2019
    • Citibank Fixed Deposit
      "GOOD"
      0.5 5.0/5 "Blown Away!"
      I have withdrawn the money so that there was a quick response also i got the money within few minutes. I used the account for more than 2 years. To open the account it is easy i have done through the online. The rate of interest was 6% per annum.
      Was this review helpful? 0
      , hyderabad
      Reviewed on Jul 18, 2019
    • SBI Fixed Deposit
      "GOOD"
      0.5 3.0/5 "Satisfactory"
      I am not much satisfied with the fixed deposit with STATE BANK OF INDIA. I am using from last few years and there is a good online banking also the service from the customer support is good added on that the overall service with them was good.
      Was this review helpful? 1
      , kolkata
      Reviewed on Jul 17, 2019
    • HDFC Bank Fixed Deposit
      "GOOD"
      0.5 4.0/5 "Great!"
      To open the account with HDFC BANK is good and simple which is easy also quick process. They are providing with the good rate of interest with the bank. The online banking i am using it is simple and easy also it is good to use. The overall service is good.
      Was this review helpful? 0
      , kolkata
      Reviewed on Jul 17, 2019
    • YES Bank Fixed Deposit
      "GOOD"
      0.5 5.0/5 "Blown Away!"
      I am having the fixed deposit with the YES BANK where the banking process was simple also to open the account it is easy and there is no locking period with the account. The customer support is good and they are with good response, overall service is good.
      Was this review helpful? 1
      , kolkata
      Reviewed on Jul 17, 2019
    • Corporation Bank Fixed Deposit
      "Comfortable Fixed deposit"
      0.5 4.0/5 "Great!"
      I have opt for five years of fixed deposit with Corporation Bank. I can invest minimum of Rs. 1000 and max amount, they are providing the current interest of 7.5% per annum but I can also prolong the duration. I have online option to deposit the fd amount, even the maturity comes along the interest to the direct account.
      Was this review helpful? 1
      , mumbai
      Reviewed on Jul 15, 2019
    • Post Office Fixed Deposit
      "Service needs to be improved"
      0.5 3.0/5 "Satisfactory"
      I do not use Post office service often because its inconvenient and they recently started the debit card service or else we need to visit to the branch for the withdrawing the money in the queue. But Post office fixed deposit interest has more interest, my mother is taking care of it.
      Was this review helpful? 1
      , gurgaon
      Reviewed on Jul 13, 2019
    • YES Bank Fixed Deposit
      "Good investment for future"
      0.5 5.0/5 "Blown Away!"
      I opened fixed deposit account in YES, as per the government rules they are providing 8% of interest on yearly basis. I am investing Rs. 50,000 per months it has the tenure period of five months, the online accessibility is good with my Yes bank.
      Was this review helpful? 0
      , kolkata
      Reviewed on Jul 11, 2019
    • HDFC Bank Fixed Deposit
      "Its satisfactory"
      0.5 4.0/5 "Great!"
      HDFC fixed deposit interest rate is very competitive as like other banks. I have activated the tenure period of one year. The online banking is convenient to manage my all investment, I can access all the information through netbanking without visiting to the bank.
      Was this review helpful? 4
      , bangalore
      Reviewed on Jun 30, 2019
    • SBI Fixed Deposit
      "PR"
      0.5 5.0/5 "Blown Away!"
      All customer can deposit the SBI fixed deposit from min of Rs. 10,000 , I believe they give 7% of interest for per annum. I have option to activate or de activate the service through online without going to the bank , there is no documentation to be signed for the online procedure. There is no charges for pre matured of FD.
      Was this review helpful? 9
      , mumbai
      Reviewed on Jun 29, 2019
    • ICICI Bank Fixed Deposit
      "Excellent service"
      0.5 5.0/5 "Blown Away!"
      I have been taken my fixed deposit ICICI bank from long time, Their service is good, i have deposit certain amount which will get mature after five years once it will get mature again i will deposit , their interest rate is less comparing to other bank.
      Was this review helpful? 3
      , chennai
      Reviewed on Jun 29, 2019
    • Punjab National Bank Fixed Deposit
      "Secured Fixed deposit"
      0.5 4.5/5 "Excellent!"
      I invested Rs. 50,000 in PNB fixed deposit it has the duration of one year then again the fixed deposit renew automatically, I am getting sms alert during the transactions. But I felt the rate of interest is lower as compared to HDFC , it would be great if they increase the interest for saving and fixed deposit.
      Was this review helpful? 3
      , bangalore
      Reviewed on Jun 29, 2019
    • HDFC Bank Fixed Deposit
      "Userfriendly Experience"
      0.5 4.0/5 "Great!"
      HDFC Bank FD is providing 7% of interest per annum, I can invest maximum of Rs.1.5 lakhs for under tax coverage. The tenure period get extend automatically after the maturity, for the tax saving FD there is five years of limit . I can deposit and withdraw the liquidity through online.
      Was this review helpful? 1
      , bangalore
      Reviewed on Jun 29, 2019
    • review Fixed Deposit
      "Awesome"
      0.5 5.0/5 "Blown Away!"
      Recently I done a Fixed Deposit on FINCARE SMALL FINANCE BANK which was referred by colleague. The policies and services are good. They are providing interest rate of 9.5% for senior citizen and the locking period is 24months. The customer service is superb.
      Was this review helpful? 5
      , ahmedabad
      Reviewed on Jun 26, 2019
    • SBI Fixed Deposit
      "Interest rates are good compared to others"
      0.5 3.0/5 "Satisfactory"
      No reason for choosing my fixed deposit account with state bank of India. They are providing a interest rate of 6.75%. I have invested the amount of Rs. 50000. There is a lockin period of 2 years. I can deposit for a long time as well. There is processing fee for my FD account.
      Was this review helpful? 6
      , kolkata
      Reviewed on Jun 24, 2019
    • Standard Chartered Bank Fixed Deposit
      "Recommendable Product"
      0.5 5.0/5 "Blown Away!"
      For the fixed deposit, Standard Chartered is providing flexible duration based on that interest may get vary. I would say its very attractive than other banks. Minimum we can invest from Rs. 10,000, the online transaction is very convenient as well.
      Was this review helpful? 1
      , noida
      Reviewed on Jun 24, 2019
    • Standard Chartered Bank Fixed Deposit
      "Recommendable Product"
      0.5 5.0/5 "Blown Away!"
      For the fixed deposit, Standard Chartered is providing flexible duration based on that interest may get vary. I would say its very attractive than other banks. Minimum we can invest from Rs. 10,000, the online transaction is very convenient as well.
      Was this review helpful? 1
      , noida
      Reviewed on Jun 24, 2019
    • Kotak Fixed Deposit
      "Good Experience"
      0.5 5.0/5 "Blown Away!"
      I activated fixed deposit through Kotak Mahindra online banking, minimum we can invest from Rs. 10,000 for the duration of one year. The interest rate is good than other bank, there is no charges for per mature liquidity. The closure procedure is very easily I can also deactivate the FD service through online.
      Was this review helpful? 3
      , chandigarh
      Reviewed on Jun 21, 2019
    • Karur Vysya Bank Fixed Deposit
      "Service is good"
      0.5 5.0/5 "Blown Away!"
      Rate of interest is little bit high compared to other bank hence i have chosen the Karur Vysya bank for my fixed deposit. I have invested the amount of Rs. 5 lakhs. They have given me a monthly interest rate of Rs. 4400. I have got a proper response from the bank. On the maturity date, i have submit the bond and get the cash.
      Was this review helpful? 3
      , chennai
      Reviewed on Jun 16, 2019
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