Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
“Interest on interest,” or the power of compound interest, is believed to have originated in 17th-century Italy. It will make a sum grow faster than simple interest, which is calculated only on the principal amount.
Compounding multiplies money at an accelerated rate and the greater the number of compounding periods, the greater the compound interest will be.
Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.
The formula for calculating the amount of compound interest is as follows:
- Compound interest = total amount of principal and interest in future (or future value) minus principal amount at present (or present value)
= [P (1 + i)n] – P
= P [(1 + i)n – 1]
Where:
P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods
Take a three-year loan of £10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be:
£10,000 [(1 + 0.05)3 – 1] = £10,000 [1.157625 – 1] = £1,576.25
The Power of Compound Interest
Because compound interest includes interest accumulated in previous periods, it grows at an ever-accelerating rate. In the example above, though the total interest payable over the three years of this loan is £1,576.25, the interest amount is not the same for all three years, as it would be with simple interest.
Compound interest can significantly boost investment returns over the long term. While a £100,000 deposit that receives 5% simple annual interest would earn £50,000 in total interest over 10 years, the annual compound interest of 5% on £10,000 would amount to £62,889.46 over the same period. If the compounding period were instead paid monthly over the same 10-year period at 5% compound interest, the total interest would instead grow to £64,700.95.
Compound Interest Schedules
Interest can be compounded on any given frequency schedule, from daily to annually. There are standard compounding frequency schedules that are usually applied to financial instruments.
The commonly used compounding schedule for savings accounts at banks is daily. For a certificate of deposit (CD), typical compounding frequency schedules are daily, monthly, or semiannually; for money market accounts, it’s often daily. For home mortgage loans, home equity loans, personal business loans, or credit card accounts, the most commonly applied compounding schedule is monthly.
There can also be variations in the time frame in which the accrued interest is credited to the existing balance. Interest on an account may be compounded daily but only credited monthly. It is only when the interest is credited, or added to the existing balance, that it begins to earn additional interest in the account.
Some banks also offer something called continuously compounding interest, which adds interest to the principal at every possible instant. For practical purposes, it doesn’t accrue that much more than daily compounding interest unless you want to put money in and take it out on the same day.
More frequent compounding of interest is beneficial to the investor or creditor. For a borrower, the opposite is true.
Compounding Periods
When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.
Compound interest can significantly boost investment returns over the long term. While a £100,000 deposit that receives 5% simple annual interest would earn £50,000 in total interest over 10 years, the annual compound interest of 5% on £10,000 would amount to £62,889.46 over the same period. If the compounding period were instead paid monthly over the same 10-year period at 5% compound interest, the total interest would instead grow to £64,700.95.
Compound Interest Schedules
Interest can be compounded on any given frequency schedule, from daily to annually. There are standard compounding frequency schedules that are usually applied to financial instruments.
The commonly used compounding schedule for savings accounts at banks is daily. For a certificate of deposit (CD), typical compounding frequency schedules are daily, monthly, or semiannually; for money market accounts, it’s often daily. For home mortgage loans, home equity loans, personal business loans, or credit card accounts, the most commonly applied compounding schedule is monthly.
There can also be variations in the time frame in which the accrued interest is credited to the existing balance. Interest on an account may be compounded daily but only credited monthly. It is only when the interest is credited, or added to the existing balance, that it begins to earn additional interest in the account.
Some banks also offer something called continuously compounding interest, which adds interest to the principal at every possible instant. For practical purposes, it doesn’t accrue that much more than daily compounding interest unless you want to put money in and take it out on the same day.
More frequent compounding of interest is beneficial to the investor or creditor. For a borrower, the opposite is true.
Compounding Periods
When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.
Recap: Definition of Compound Interest
Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially—rather than linearly—over time. The key word here is compound.
Suppose you make a £100 investment in a business that pays you a 10% dividend every year. You have the choice of either pocketing those dividend payments like cash or reinvesting them into additional shares. If you choose the second option, reinvesting the dividends and compounding them together with your initial £100 investment, then the returns you generate will start to grow over time.
Who Benefits From Compound Interest?
Compound interest benefits investors, but the meaning of investors can be quite broad. Banks, for instance, benefit from compound interest when they lend money and reinvest the interest they receive into giving out additional loans. Depositors also benefit from compound interest when they receive interest on their bank accounts, bonds, or other investments.
It is important to note that although the term compound interest includes the word interest, the concept applies beyond situations for which the word is typically used, such as bank accounts and loans.