# Compound Interest Formula and Benefits

“Compound interest is the eighth wonder of the world. Whoever understands it, earns it; whoever doesn’t, pays for it.

Albert Einstein would have said that. Many quotes are attributed to him that he did not actually say, and this may be one of them; Personally, I don’t see the guy who imagined riding a beam of light to understand the poetic relativity theory of compound interest.

But even though Einstein didn’t actually say compound interest was the eighth wonder of the world, it’s still a good point. Compound interest East really great. It is a powerful concept, which can powerfully strengthen or weaken your finances. The man who understands this will have a tool to increase his net worth; the man who won’t spend his life stuck in a paycheck mentality.

My seven-year-old son recently opened a savings account, and this allowed me to explain compound interest to him. It didn’t go well. It’s one of those financial concepts that is so simple you take it for granted. Therefore, when you have to explain it to a child, you realize that you don’t understand it as much as you thought. Einstein is also said to have said, “If you can’t explain it to a six-year-old, you don’t understand it yourself.” Again, even though he didn’t say that, that’s a good point.

If your dad never sat you down to talk about compound interest, you’re in luck; having refined my explanation of Gus, I will now pass it on to you.

### What is compound interest?

To understand compound interest, it helps to first understand simple interest.

Simple interest is calculated on the principal or original amount of a deposit or loan. It’s really, well, simple to understand.

Let’s say you take out a \$10,000 loan at a simple interest rate of 5%. The term of the loan is four years.

To calculate the interest that will accrue on the loan, you will use the following formula:

Principal x interest rate x term of the loan

Plugging in our numbers, that would be:

\$10,000 x 0.05 x 4 = \$2,000

So that \$10,000 loan will cost you \$2,000 in simple interest.

Car loans, home loans, and student loans use simple interest. A loan you take from a family member or friend will likely use simple interest (if they charge you interest).

Now that you understand simple interest, we can move on to compound interest.

Compound interest is calculated on the principal amount and, crucially, also on accrued interest from previous periods. It’s interest on interest.

This is what the compound interest formula looks like:

P(1+r/n) (NT) –P

[P = Principal; r = annual interest rate in percentage terms; n = number of compounding periods for a year; t = number of years money is invested or borrowed]

Yes, this sounds confusing, but let’s insert our numbers from the simple interest example to see what we would pay if interest were compounded.

So we got a loan of \$10,000 which accumulates annually at 5 %. The term of the loan is 4 years. What would we pay in interest? Let’s look at the progression of mathematics:

\$10,000 (1+0.05/1)(1×4) – \$10,000 →

\$10,000 (1+0.05/1)(4) – \$10,000 →

\$10,000 (1.21550625) – \$10,000 →

\$12,155.0625 – \$10,000 = \$2,155.06

So, on a four-year loan compounded annually, we would pay \$2,155.06 in compound interest. That’s \$155.06 more than a simple interest loan. Calculating interest on interest already accrued on a principal can really add up. And add quickly as we will see in an example below.

If you’d rather not do the math yourself, there are plenty of compound interest calculators in line.

Credit cards calculate balances on compound interest. Instead of compounding annually, credit card companies compound monthly. Credit cards’ high interest rates coupled with their monthly capitalization are why almost every personal finance gurus says, “Don’t keep a balance on your credit cards!” You end up paying a lot for that extended credit. For example, a credit card balance of \$10,000 carried at an interest rate of 20% (compounded monthly) would result in a total compound interest of \$2,193.91 over one year, or approximately \$183 per month. Imagine what you could do with an extra \$183 per month.

However, compound interest can work in your favor. Highligths. When you put your money in a savings account, banks usually pay compound interest daily on the money you keep with them. Granted, the interest rate you get is pretty crappy – somewhere between 0.03% and 1% depending on the bank – but when you dial in at that rate daily and hold that money for a long time, things can get ugly. add.

If you invest in an index fund, you can take advantage of the power of compound interest by reinvesting your earnings into buying more of the index fund, which will earn you even more, which you then reinvest. etc right now.

### Capitalization periods have a significant effect on earnings

Looking at the compound interest formula, you’ll probably notice that the frequency of the calculation periods can have a big effect on your earnings or how much you have to pay in interest. The more compounding periods, the higher the accrued interest. You will earn more interest from a bank that compounds daily compared to a bank that compounds only monthly; you will pay more interest on a loan compounded monthly than on a loan compounded annually.

So when looking at interest rates for a savings account or loan, be sure to pay attention to how often the interest is compounded.

The real magic of compounding is revealed over long periods of time. The longer you let your money stay in an account and accumulate, the more money you earn.

This is the big point that I tried to make my son understand. What helped light the light bulb in his head is this example from personal finance expert Beth Kobliner:

If you were to save \$1,000 a year from age 25 to 34 in a retirement account earning 8% a year and never invest a penny more, your \$10,000 investment would grow to \$157,435 at age 65. . But if you don’t start saving until you’re 35 and invest \$1,000 a year for the next 30 years (that’s a total investment of \$30,000), you’ll only have \$122,346 at 65 years. pile up.

Understanding this concept helped turn Gus into a tight-fisted Scrooge McDuck. “Man, imagine how much interest I can earn since I started at seven!” At the start of each month, he likes to check his savings account to see how the interest he’s earning is slowly increasing thanks to the magic of compound interest.