More Detail with Compound Interest…

Disclaimer: None of this is advice.; it’s for educational purposes only. Questions and/or thoughts? Drop me a line and let’s discuss.

Ooo, buddy-buddy, this is where it starts to get super interesting! The concept of compound interest is pretty cool once we begin to understand just how powerful the idea is. So what is it? Well, It’s exactly what the name implies: It is an interest payment being paid that continues to “compound” on top of what was previously contributed / added / paid. While the amount we initially contribute and the interest rate earned are relevant details we also need to factor in one of the most important variables: Time. Time will be the variable we really focus on today, and "time" is what really allows compound interest to spread its wings and shine. Meaning what? To allow “compounding” to work at its most powerful is to allow the contribution or principal the “time” to compound and grow. That is precisely why we hear so many economists, planners, and advisors talk about starting early with investing and saving. That can seem a little abstract so let’s break it down a little simpler with real numbers.

Let's say you invest $100 at the beginning of the “term”, or time period, to an account paying 10% interest and at the end of the year you get a $10 interest payment. You leave the full $110 in the account and another year later (2 years after the initial contribution or investment) you get the 10% interest payment not just on the original $100 but on the $110. So this interest payment is $11. Seems kind of minuscule, right? ‘

How it maths out:

Initial contribution = $100

Interest Rate = 10%

Interest payment end of year 1: $100 * 10% = $10 (add this to our initial contribution)

Account Value After First Interest Payment = $110

Interest payment end of year 2: $110 * 10% = $11

Total interest payments paid in total after 2-year investment = $21.

Total Account Value After 2 years of intest payments = $121

Notice how the interest payment amount grew a little at the end of year two? That’s because you’re earning interest on your interest. We were paid 10% on the initial contribution at the end of year 1 and 10% on the initial contribution plus the first interest payment at the end of year 2.

Ok, seems simple enough. So is that it? Yes, kind of but let’s peek a little more behind the curtain of this compounding power. And let’s do this by identifying the key factors that make compound interest work (yes, the dollar amount we start with absolutely plays a role but most of us start with small investments in the beginning):

Time - The longer you leave your money invested, the more dramatic the effect becomes. Starting early makes a huge difference.

Interest rate - Higher rates mean more growth, but even small differences in rates can add up significantly over time.

Frequency - Interest that compounds daily grows the total amount faster than interest that compounds annually. (We’ll cover this in more detail in a different post to avoid any confusion because the frequency of compounding can hit the gas pedal on compounding.)

Our previous mini-illustration does an ok job, but let’s take a look at some additional examples with a little more detail to illustrate what happens when we modify one of the three variables of: Time, Principal, and Interest Rate. We’ll keep a 10% interest rate for the upcoming examples. In reality, 10% interest payments are relatively high and not too common without taking on higher levels of risk but it helps to show how the math works and how important the concept is (we’ll cover what “risk” means in a subsequent post).

(A financial calculator or the compound interest formula can be utilized to find the following “Future Values” of the initial principal. Compound interest formula? Huh?! That would be this guy:

Compound Interest formula is: A = P (1+r/n) , where:

A = total amount after interest,

P = the principal amount,

r = the annual interest rate (in decimal),

n = the number of times interest is compounded

per year, ex.: annual = 1, quarterly = 4;

monthly = 12, etc.;

t = the number of years the money is invested or borrowed.

This formula calculates and gives us the total ending value including both the principal and the interest earned or paid.

Remember, these illustrations do not take into consideration additional contributions made to the account; just the original contribution. Also, we are using these three terms to be interchangeable throughout this exercise: Initial investment = Principal = Contribution.

Example #1

P, Principal = $1000

t, Time = 10 years

i, Interest rate = 10%

FV, Future Value = $2593.74

Annual Schedule: This table shows what the formula calculates at the very bottom right (Ending Balance, Row 10), but also shows the total interest paid over the course of 10 years (Interest Paid, Row 11).

Year	Deposit	Interest Paid	Ending balance
1	$1,000.00	$100.00	$1,100.00
2	$0.00	$110.00	$1,210.00
3	$0.00	$121.00	$1,331.00
4	$0.00	$133.10	$1,464.10
5	$0.00	$146.41	$1,610.51
6	$0.00	$161.05	$1,771.56
7	$0.00	$177.16	$1,948.72
8	$0.00	$194.87	$2,143.59
9	$0.00	$214.36	$2,357.95
10	$0.00	$235.79	$2,593.74
11	Total Interest Paid	$1,593.74

Example #2 — Let’s make a change to the “time” and double it so the contribution is held for 20 years instead of 10 years..

P, Principal = $1000

t, Time = 20 years

i, Interest rate = 10%

FV, Future Value = $6727.50

Annual Schedule: This table shows what the formula calculates at the very bottom right (Ending Balance, Row 20), but also shows the total interest paid over the course of 20 years (Interest Paid, Row 21).

Year	Deposit	Interest Paid	Ending balance
1	$1,000.00	$100.00	$1,100.00
2	$0.00	$110.00	$1,210.00
3	$0.00	$121.00	$1,331.00
4	$0.00	$133.10	$1,464.10
5	$0.00	$146.41	$1,610.51
6	$0.00	$161.05	$1,771.56
7	$0.00	$177.16	$1,948.72
8	$0.00	$194.87	$2,143.59
9	$0.00	$214.36	$2,357.95
10	$0.00	$235.79	$2,593.74
11	$0.00	$259.37	$2,853.12
12	$0.00	$285.31	$3,138.43
13	$0.00	$313.84	$3,452.27
14	$0.00	$345.23	$3,797.50
15	$0.00	$379.75	$4,177.25
16	$0.00	$417.72	$4,594.97
17	$0.00	$459.50	$5,054.47
18	$0.00	$505.45	$5,559.92
19	$0.00	$555.99	$6,115.91
20	$0.00	$611.59	$6,727.50
21	Total Interest Paid	$5,727.49

**(There is a $0.01 difference in the values due to a rounding error in the calculations when you go row by row vs. utilizing the formula. Basically, rounding to two decimal places for each calculation.)

Example #3 — Lastly, let’s triple the time the initial contribution is held from 10 years to 30 years.

P, Principal = $1000

t, Time = 30 years

i, Interest rate = 10%

FV, Future Value = $17,449.40

Annual Schedule: This table shows what the formula calculates at the very bottom right (Ending Balance, Row 30), but also shows the total interest paid over the course of 30 years (Interest Paid, Row 31).

Year	Deposit	Interest	Ending balance
1	$1,000.00	$100.00	$1,100.00
2	$0.00	$110.00	$1,210.00
3	$0.00	$121.00	$1,331.00
4	$0.00	$133.10	$1,464.10
5	$0.00	$146.41	$1,610.51
6	$0.00	$161.05	$1,771.56
7	$0.00	$177.16	$1,948.72
8	$0.00	$194.87	$2,143.59
9	$0.00	$214.36	$2,357.95
10	$0.00	$235.79	$2,593.74
11	$0.00	$259.37	$2,853.12
12	$0.00	$285.31	$3,138.43
13	$0.00	$313.84	$3,452.27
14	$0.00	$345.23	$3,797.50
15	$0.00	$379.75	$4,177.25
16	$0.00	$417.72	$4,594.97
17	$0.00	$459.50	$5,054.47
18	$0.00	$505.45	$5,559.92
19	$0.00	$555.99	$6,115.91
20	$0.00	$611.59	$6,727.50
21	$0.00	$672.75	$7,400.25
22	$0.00	$740.02	$8,140.27
23	$0.00	$814.03	$8,954.30
24	$0.00	$895.43	$9,849.73
25	$0.00	$984.97	$10,834.71
26	$0.00	$1,083.47	$11,918.18
27	$0.00	$1,191.82	$13,109.99
28	$0.00	$1,311.00	$14,420.99
29	$0.00	$1,442.10	$15,863.09
30	$0.00	$1,586.31	$17,449.40
	Total Interest Paid	$16,449.40

Look at that! No additional contributions. Just $1000 deposited in a 10% interest paying or “interest-bearing” account for 10, 20, 30 years and allowing “time” to work.

Great. Wonderful. A bunch of numbers in tables. What does all this mean? What is the point?

The Compound Interest Healthy Bits

This is one of the most powerful concepts in finance, and understanding it can really help with our financial decisions. If we’re investing and saving then a higher interest rate is what we want but we’re not a big fan of higher interest rates when it’s for a loan we’re having to pay back. We have to find the balance that allows us the best financial path forward.

At its core, compound interest means you earn interest not just on your original money, but also on the interest you’ve earning along the way. Think of it like a snowball rolling down a hill - it starts small but keeps getting bigger as it picks up more snow.

This is why financial advisors often say “time in the market beats timing the market” and why starting to save and invest early, even with small amounts, can be so remarkably powerful for building wealth.​​​​​​​​​​​​​