What is Interest?
When it comes to calculating interest, there are two basic choices: simple and compound.
Simple interest simply means a set percentage of the principal every year.
Simple Interest, I = P x R x T
- P = Principal Amount
- R = Interest Rate
- T = # of Periods
Got it. Simple right?
I know, not at ALL!
For something that has simple in it, it ain’t so simple 😕
Here are some simple examples.
Mr. Leo plans to place his money in a certificate of deposit that matures in three months. The principal (amount invested) is $10,000 and 5% interest is earned annually.
He wants to calculate how much interest he will earn in those three months.
I = P x R x T
I = $10,000 x 5%/year x 3/12 of a year
I = $125
Laura wants to borrow money from her mother, and she is offered a five-year, non-compounding loan of $7,000, with a 3% annual interest rate.
What is Laura’s total interest expense?
I = P x R x T
I = $7,000 x 3%/year x 5 years
I = $1,050
Below are some other forms of real-world simple interest examples.
Bonds pay non-compounding interest in the form of a coupon payment. These coupon payments are not automatically reinvested/compounded and therefore are an example of simple interest.
It may be surprising to learn that most mortgages are based on non-compounding interest.
Even though the principal payments vary, the interest is always considered as currently paid in full, and thus there is no compounding effect on the interest itself.
Now to the reason you’re here! Compound Interest!
Compound interest refers to interest payments that are made on the sum of the original principal and the previously paid interest.
An easier way to think of compound interest is that is it “interest on interest,” where the amount that the interest payment is based on changes in each period, rather than being fixed at the original principal amount.
Compound interest is applied to both loans and deposit accounts. Compound interest is the reason many investors are so successful.
The formula for compound interest, including principal sum, is:
A = P (1 + r/n) (nt)
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for
It’s worth noting that this formula gives you the future value of an investment or loan, which is compound interest plus the principal.
Should you wish to calculate the compound interest only, you need to deduct the principal from the result. So, your formula would look like this:
Compounded interest only = P (1 + r/n) (nt) – P
If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows…
P = 5000.
r = 5/100 = 0.05 (decimal).
n = 12.
t = 10.
If we plug those figures into the formula, we get the following:
A = 5000 (1 + 0.05 / 12) (12 * 10) = 8235.05.
So, the investment balance after 10 years is $8,235.05.
The 4 Components of Compound Interest
The principal is the amount that is originally deposited in a compounding environment (for example, a high-interest savings account at a bank). It is the starting amount upon which the first interest payment is calculated from.
2. Interest rate
The interest rate refers to the rate that is paid on the account value. The interest payment will be equal to the interest rate times the account value (which is the sum of the original principal and any previously paid interest).
3. Compounding Frequency
The compounding frequency determines how many times a year the interest is paid. It will influence the interest rate itself as high-frequency compounding will typically only be available with lower rates. Typically, compounding occurs on a monthly, quarterly, or annual basis.
4. Time horizon
Time horizon refers to the amount of time over which the compound interest mechanism can operate.
The longer the time horizon, the more interest payments that can be made to the original principal and the larger the ending account value will be.
Time horizon is the single most important component of compound interest, as it essentially dictates the future profitability of an investment.
Practical Example: Compound Interest
Jack wants to start saving and decides to deposit money into a high-interest savings account. He deposits an initial $20,000, which is to be compounded yearly at a rate of 3% per month.
Jack is currently 20 years old and plans to retire at 60, which means he has a 40-year time frame to accumulate interest.
Taking into account the given information, the table below calculates how much Jack’s account value would be at the end of his time horizon:
We see that the account value at the end of the 40-year period is about $70,000. It shows the power of compound interest, because Jack was able to multiply his money 7x without actively managing the investment.
The example above also assumes that Jack never deposited additional money into his savings account.
Had Jack deposited an additional $20,000 early on in his time horizon, the final account value would have been dramatically higher.
The “Time” Factor
If you’re under the age of 35, you have one of the biggest advantages out there when it comes to planning for retirement or financial freedom.
How much you can put away per month is important but, as the numbers show below, that number pales in comparison to how much time you can invest in your plan.
In other words, the sooner you start, the greater the advantage you’ll have.
Don’t believe it?
Check out the chart below, which plots the savings strategies of three fictional investors, each of whom saved the same amount of money over a 10-year term.
Through an incredible stroke of investment luck, each earned the same average annual return (seven percent) consistently, until age 65.
The only difference between these investors is the year they started.
If you plan to retire, you will be amazed by the results.
Black Magic is at Work
Michael saved $1,000 per month from the time he turned 25 until he turned 35. Then he stopped saving but left his money in his investment account where it continued to accrue at a seven percent rate until he retired at age 65.
Jennifer held off and didn’t start saving until age 35. She put away $1,000 per month from her 35th birthday until she turned 45. Like Michael, she left the balance in her investment account, where it continued to accrue at a rate of seven percent until age 65.
Sam didn’t get around to investing until age 45. Still, he invested $1,000 per month for 10 years, halting his savings at age 55. Then he also left his money to accrue at a seven percent rate until his 65th birthday.
Michael, Jennifer, and Sam each saved the same amount — $120,000 — over a 10 year period.
Sadly for Jennifer, and even more so for Sam, their ending balances were dramatically different.
How do I save that much?
I know what you’re thinking.
$1,000 per month sounds like a lot for a 25-year-old to save!
I hear you. It is.
For a majority of people, this isn’t feasible. However, let’s say it is.
According to the National Center for Education Statistics, the median annual earnings for a college-educated young adult (aged 25-34) is $46,900. At that income level, a $12,000 annual investment represents 25.5 percent of income.
That’s no small percentage, but that’s before the tax advantages of your employer’s retirement plan are considered.
If your employer offers a 401(k), 403(b), or some other tax-advantaged retirement plan, the money you put away is invested on a pre-tax basis.
This means you won’t pay income taxes on your retirement savings until you take the money out at retirement (when your income and your tax burden will be lower).
What does this mean?
If you’re putting away $12,000 a year in your company’s 401(k) plan, you’re not actually losing that full amount from your take-home pay.
Instead, assuming you’re paid every two weeks, your take-home pay will reflect a $346 decrease, assuming you’re a single tax filer in the 25 percent tax bracket.
Thanks to the power of compound interest (the investing magic that allows investment earnings to earn interest of its own), time is the most powerful variable a young investor has on his or her side.
Your baby boomer parents might bring home a much higher income, but if you start now, the amount you’ll have to save to fund your own retirement is dramatically lower.
Almost $350 per pay period isn’t chump change, but it is do-able. In fact, do it for 10 years and you might choose to never do it again. You might not have to.
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