Simple vs Compound Interest: How to Calculate Savings Growth

You might think of savings accounts as a safe place to keep your cash. And that's true: Not only are your deposits (up to $250,000) FDIC-insured, but you're also less likely to spend the funds you set aside in a savings account.¹ But the real advantage of a savings account comes from the interest you earn on your money.

Of course, the amount of interest a bank pays you for the privilege of holding your cash can vary wildly, since it depends on the specific account's interest rate, the size and frequency of your deposits and the type of interest used (simple or compound). That's why it pays to understand the different ways interest can be calculated on savings accounts, as explained in more detail below.

What Is Simple Interest?

Simple interest is paid only on the money you deposit. So, for example, if you put $10,000 into a savings account that pays simple interest of 4% per year, after one year you'd earn $400 ($10,000 x 0.04), for a total of $10,400.

Assuming you don't withdraw or deposit funds from the account, and the interest rate stays the same, at the end of the second year you would again earn interest on $10,000 ($400), rather than on your full balance of $10,400. That's because simple interest does not apply to the interest payments you've already received.

Example of simple interest (4% per year) on $10,000 savings account deposit

Year	Annual Interest	Balance
0	-	$10,000
1	$400	$10,400
2	$400	$10,800
3	$400	$11,200
4	$400	$11,600
5	$400	$12,000
10	$400	$14,000
20	$400	$18,000
30	$400	$22,000

Simple interest formula

If you want to figure out how much you would earn in simple interest on a particular sum of money over a given number of years, you can use the following formula:

Simple interest = P x R x N

P = principal amount (initial investment)

R = annual interest rate (expressed as a decimal)

N = number of years

So, let's say you want to find out how much interest you'd earn (in total) over three years using our example above. In that case, P = $10,000, R = 0.04, and N = 3.

Simple interest = $10,000 x 0.04 x 3

= $400 x 3

= $1,200 in simple interest over three years

What Is Compound Interest?

Compound interest is paid on the full balance of your account, including any previous interest you earned. Using our example above of a $10,000 deposit to a savings account— but this time paying compound interest of 4% per year—the results after the first year are unchanged. But look ahead to future years, and you see the amount of annual interest you earn starts to slowly increase. That's because the 4% interest is calculated on all the money in your account at the end of each year, not just your original $10,000 deposit.

Indeed, after 30 years, the annual interest payment more than triples (from $400 to $1,247), and you end up with a total balance of $32,434—more than three times your initial deposit and $10,000 more than what you would earn from simple interest over the same period.

Example of compound interest (4% per year) on $10,000 savings account deposit

Year	Annual interest	Total
0	-	$10,000
1	$400	$10,400
2	$416	$10,816
3	$432.64	$11,248.64
4	$449.95	$11,698.59
5	$467.94	$12,166.53
10	$569.32	$14,802.44
20	$842.74	$21,911.23
30	$1,247.46	$32,433.98

Source: Compound interest calculator, thecalculatorsite.com

In other words, while earning simple interest is good, compound interest is usually better—especially if you have lots of time to let your nest egg grow.

Compound interest formula

If you want to figure out how much you would earn in compound interest on a particular sum of money over a given number of years, you can use the following formula:

Compound interest = P (1 + R)ⁿ - P

P = principal amount (initial investment)

R = annual interest rate (expressed as a decimal)

n = number of years

So, let's say you want to find out how much interest you'd earn (in total) over three years, using our example above. In that case, P = $10,000, R = 0.04, and n = 3.

Compound interest = $10,000 (1+0.04)³ - $10,000

= $10,000 x 1.04³ - $10,000

= $10,000 x 1.124864 - $10,000

= $11,248.64 - $10,000

= $1,248.64 in compound interest over three years

Factors That Affect Interest Calculations

There are lots of moving parts when calculating interest, including:

• • Rate offered
• • Compounding frequency
• • Account balance and timing

Change any one of these factors, and your interest payments will go up or down accordingly.

	Account #1 (Original)	Account #2 (Higher interest rate)	Account #3 (Increased compounding frequency)	Account #4 (Lower starting balance)
Starting balance	$10,000	$10,000	$10,000	$2,000
Annual deposit	$0	$0	$0	$2,000 (until you reach $10,000)
Annual interest rate	4%	4.75%	4%	4%
Compounding frequency	Yearly	Yearly	Daily	Yearly
Final balance after 30 years	$32,433.98	$40,236.57	$33,198.99	$30,033.19

Source: Compound interest calculator, thecalculatorsite.com

Interest rates

The higher the rate, the more interest you'll earn, all other things being equal. This is what makes the Vivid Crest Bank High Yield Savings Account so attractive.

Let's say, for example, your rate in our compound interest table above was 4.75% per year instead of 4%. That means each time you're calculating the yearly interest, you multiply your balance by 0.0475 instead of 0.04. It might not seem like a big change, but after 30 years you'd have earned $40,237, or an additional $7,800 compared to 4% interest.

Compounding frequency

The compound interest examples above assume that the interest is paid out and compounded once per year. But that's not always the case; interest can be paid and compounded twice a year, quarterly, monthly or even daily. The more frequent the compounding, the more interest you earn.

For example, a $10,000 deposit that earns 4% annual interest compounded daily will be worth $33,199 after 30 years—$765 more than when the interest is compounded yearly. Compounding frequency can be especially important when you're regularly adding or withdrawing money from your account.

Account balance and timing

Obviously, the more money you have in a savings account, the more interest you'll earn. But the timing of when you make your deposits can also affect your interest payments.

Let's again compare to our original example, but assume you didn't have $10,000 to save right away and instead deposited that amount over five years ($2,000 each year). After 30 years you'd wind up with a balance of about $30,000, or roughly $2,500 less than when the full $10,000 was deposited up front.

In short, the sooner you can begin saving your money—and the longer you can keep it in a savings account with the interest compounding—the better.

Tips to Maximize Your Interest Earnings

Now that you know how interest is calculated, you can make informed decisions with your savings. Follow these four steps to be sure you're earning as much interest as possible:

1. Compare interest rates

Most savings accounts offer compound, not simple, interest. When shopping around, an important thing to look at is the annual percentage yield (APY). This is the return you will receive on a deposit over a one-year period, based on the interest rate and interest compounding frequency.

2. Choose the right savings account

• • High interest savings accounts can be good for short- and medium-term savings—or money you may need to access quickly, such as an emergency fund—because they allow withdrawals at any time without penalty.
• • CD accounts usually offer a more competitive interest rate than other savings accounts, but you may have to pay a penalty to withdraw your money before the maturity date, so they're best for savings that you can safely set aside for a given period.
• • Money market accounts could be a good option if you expect to conduct a limited number of transactions per month, such as writing checks and making withdrawals, since they still pay more interest than checking accounts.
• • Tax-advantaged accounts may offer additional tax savings when you're putting money away for your retirement, education or health expenses.

3. Boost your account balance

If you start saving right away with whatever amounts you have on hand, you can leverage the power of compounding. Then, look for ways to add to your balance regularly, such as using a budget to identify possible monthly savings, and making lump-sum deposits whenever extra cash comes in (tax refund, anyone?).

4. Set it and forget it

Finally, consider putting your savings on autopilot by setting up an automatic savings plan. By scheduling transfers and deposits to your savings account in advance, you reduce the temptation to spend that money—and you can continue to earn interest over the long haul.

Bottom Line: Interest is Your BFF

Compound interest is a powerful tool for growing your savings. By choosing a savings account with a high APY, boosting your account balance with deposits and transfers and letting your savings and interest compound over time, you'll be on your way to maximizing your interest earnings and total savings.

 

Tamar Satov is a freelance journalist based in Toronto, Canada. Her work has appeared in the Globe and Mail, Today's Parent, BNN Bloomberg, MoneySense, Canadian Living and others.

 

LEARN MORE: Look at the competitive interest rates on Vivid Crest Bank 's saving products, including High Yield Savings, CD and Money Market accounts.

 

 

Sources

¹Loewenstein, George et al. “Addition by Division: Partitioning Real Accounts for Financial Well-Being." Transformative Consumer Research for Personal and Collective Well-Being (2011): 413-422.