Some people like to refer to the principle of compound interest as magical – and while it's not magical, it is a pretty cool mathematical principle.
Compound interest is what happens when the interest you earn on savings begins to earn interest on itself. As interest grows, it begins accumulating more rapidly and builds at an exponential pace. The potential effect on your savings can be dramatic.
How compound interest works
Imagine you contribute $1,000 to a hypothetical investment that earns eight percent annually.
After the first year, your balance is $1,080.
The next year, you contribute another $1,000 and earn eight percent again – not only on your contributions (called the “principal”) of $2,000, but also on the interest from the first year ($80).
Let's do the math for the second year of your account.
- Starting value is $1,080 (your principal and interest from Year 1)
- + $1,000 (your Year 2 principal contribution)
- = $2,080 (Year 1 total + Year 2 principal)
- + $166.40 (8 percent of $2,080, your Year 2 interest)
- = $2,246.40 (your new total balance)
Now, we'll repeat the same formula for the third year.
- Starting value is $2,246.40
- + $1,000 (your Year 3 principal contribution)
- = $3,246.40 (Year 2 total + Year 3 principal)
- + $259.71 (8 percent of $3,246.40, your Year 3 interest)
- = $3,506.11 (your new total balance)
See how things can add up quickly? That's the power of compounding!
The effect of compound interest over time
In the early years of saving, it may seem like you’re earning only a modest amount of interest, but give it time.
With each passing year, your compounding interest grows exponentially until it exceeds your principal and is responsible for most of the growth in your account.
The chart below is based on our examples above and shows what the combination of time and compound interest can potentially do.
FAQs
Compound interest is interest that is calculated on the principal investment in an account, as well as on any returns earned over time. As brokerage accounts or savings accounts earn interest, those new amounts are added to the original principal amount.
How does the compound interest work? ›
Compound interest builds on the principal balance plus accrued interest. If you have $1,000 at a 2% interest rate compounded annually, you'll earn $20 interest in year 1, and $20.40 interest in year 2 since you have $1,020 in your account after the first year.
What is the answer to the compound interest? ›
The compound interest is found using the formula: CI = P( 1 + r/n)nt - P. In this formula, P( 1 + r/n)nt represents the compounded amount. the initial investment P should be subtracted from the compounded amount to get the compound interest.
How do you solve compound interest questions easily? ›
A = P (1+ r/n)nt
- 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.
Compound Interest: Interest earned is added to the principal, forming a new base on which the next round of interest is calculated. This can accrue daily, monthly, or quarterly.
How do I calculate compound interest? ›
The formula we use to find compound interest is A = P(1 + r/n)^nt. In this formula, A stands for the total amount that accumulates. P is the original principal; that's the money we start with. The r is the interest rate.
How do I compound my money? ›
Compounding is a powerful investing concept that involves earning returns on both your original investment and on returns you received previously. For compounding to work, you need to reinvest your returns back into your account.
How to earn compound interest daily? ›
Money market accounts (MMAs)
A money market account is another type of savings account. It's like a cross between a checking and a savings account. Like a high-yield savings account, you usually get better rates than you would in other types of interest-bearing accounts. Typically, money market accounts compound daily.
How to calculate compounded return? ›
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 principal or amount of the loan is then subtracted from the resulting value. Katie Kerpel {Copyright} Investopedia, 2019.
How do you explain compound interest with examples? ›
Let's say you have $1,000 in a savings account that earns 5% in annual interest. In year one, you'd earn $50, giving you a new balance of $1,050. In year two, you would earn 5% on the larger balance of $1,050, which is $52.50—giving you a new balance of $1,102.50 at the end of year two.
Basic compound interest
For other compounding frequencies (such as monthly, weekly, or daily), prospective depositors should refer to the formula below. Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.
What is the secret formula for compound interest? ›
Interest Compounded for Different Years
| Time (in years) | Amount | Interest |
|---|
| 2 | P ( 1 + R 100 ) 2 | P ( 1 + R 100 ) 2 − P |
| 3 | P ( 1 + R 100 ) 3 | P ( 1 + R 100 ) 3 − P |
| 4 | P ( 1 + R 100 ) 4 | P ( 1 + R 100 ) 4 − P |
| n | P ( 1 + R 100 ) n | P ( 1 + R 100 ) n − P |
1 more rowHow to avoid compound interest. To minimise the amount of compound interest you pay, there is one effective strategy: pay off the loan as quickly as you can. Let's consider an example similar to the scenario mentioned in the TikTok video – a mortgage with a loan term of 20 years.
What is the rule of 72 backwards? ›
You can also run it backwards: if you want to double your money in six years, just divide 6 into 72 to find that it will require an interest rate of about 12 percent. where Y and r are the years and interest rate, respectively.
What does compound interest work? ›
Compound interest is when you earn interest on the money you've saved and on the interest you earn along the way. Here's an example to help explain compound interest. Increasing the compounding frequency, finding a higher interest rate, and adding to your principal amount are ways to help your savings grow even faster.
How to calculate simple vs compound interest? ›
Simple interest is calculated by multiplying the loan principal by the interest rate and then by the term of a loan. Compound interest multiplies savings or debt at an accelerated rate. Compound interest is interest calculated on both the initial principal and all of the previously accumulated interest.
What is $15000 at 15 compounded annually for 5 years? ›
The time period T = 5 years. A = $30,170.36 hence, the total amount after 5 year will be $30,170.36.
What will be the compound interest on $25,000 after 3 years at 12 per annum? ›
What will be the compound interest on a sum of Rs. 25000 after 3 years at the rate of 12 per cent p.a.? Rs. 10123.20.
Can you lose on compound interest? ›
o Compounding interest works for the investor when the portfolio is making gains, but works against the investor when losses occur. o When minimizing losses in your investment and trust portfolios, your wealth compounds from a higher floor and this is the key to long-term wealth creation.
