Difference between simple and compound interest

Interest

Difference between simple and compound interest is relatively easy to explain. Simple interest is the amount of interest gained off on the principle invested one time. Compound interest is the interest on the principle and interest combined.

A savings account is a great example of compound interest, because every quarter or every year your bank pays you dividends on the amount of money you keep in your savings account. Usually savings account percentages are between .25% to .40% average APY (Average Percentage Yield). Some specialized savings account can get up to .80%, but usually require a higher minimum amount to open those accounts.

A loan is a good example of simple interest, as the amount of interest calculated is based on the original amount that you barrow. Most loans can range between 0% up to 25% (legal max for loans in Florida, max may be different in your state) interest rate.

The amount of the loan will also determine how much interest you can be charged. Often the larger the loan the more the creditor can charge.

Calculating Interest

When calculating interest rates it is always easier to calculate simple interest than it is to calculate compound interest, because simple interest is only one calculation.

For example if you take a loan for $10,000 at a 12% APR (Annual Percentage Rate) you would owe the bank $11,200 if you pay for the full length of the loan; however, if you pay the loan off sooner than the percentage rate schedule you would end up paying less. The reason you would pay less is that 12% interest rate broken down to a monthly rate, so if you pay extra every month than you will end up paying less than the full 12% interest rate.



This is the formula you would use to calculate your interest for a one year loan of $10,000 at 12%.

  • I(nterest) = P(rinciple) x R(ate) x T(ime)
  • $1,200 = $10,000 x .12 x 1
  • $10,000 + $1,200 = $11,200

If you want to know your monthly interest rate over the course of the loan you would simply divide 12% by however many months you have the loan for.

For Example if you have a 5-year loan term:

  • 5 [years] x 12 [months] = 60 [months]
  • 12% [Interest] / 60 [months] = .002%
  • $10,000 x .002% = $20 [Interest per month]
  • $10,000 / 60 [months] = $166.67 [payment per month] + $20 [Interest per month] = 186.67 [monthly payment]

Now for compound interest that is a bit more difficult to calculate, because several factors come into the equation. For example, you start a savings account with $500 and left it there for 10 years. The interest on that account can also possibly vary from one quarter to the next depending on the type of account.

The compound interest formula:

  • C(ompound Interest) = P(rinciple {Originally}) [(1 + r{ate per period})n(umber of periods) -1]
  • Total compounded interest = P (1 + r/n) ^(nt) – P
  • $823.50 = 500[(1 + 0.05 / 12)(12 x 10)]

*The up arrow symbol “^” is used to denote the power of. For example: 10^2 would equal to 100.*

Now to that account you add $10 every week which means that the principle is always changing, that is calculated differently. As an example we will use the same savings account as above and to that $500 we will add an additional $10 per week (payday).

There are two distinct formulas for this, and it is based on when the payment is made to the account. If you pay the full $40 of savings at the beginning of the month, quarter, or year it will require one formula. If you make those payments at the end of the period than you will use a different formula.

The formula for payments at the end of the term is as follows.

  • [P(1+r/n)(nt) ] + [ PMT (monthly payment) × {[(1 + r/n)(nt) – 1] / (r/n)} ]
  • {[$500 (1 + .05/12)^(12 x 10) ] + [ $40 x {(1 + .05/12)^(12 x 10) – 1} / (.05/12)) ]}
  • {[$500 (1.0041666)^(120) ] + [ $40 x {(1.0041666)^(120) – 1} / (.0041666)) ]}
  • $823 + $6211.02 = $7034.02

Somewhere I was off on my math as you can see below the results of depositing at the end of the term.

 

If you are wondering what it would be if you made your deposits at the beginning of the term that formula is below. I’m not even going to embarrass myself trying to figure out that problem.

  • PMT × {[(1 + r/n)(nt) – 1] / (r/n)} × (1+r/n)

As you can see if you invest your money regularly with a decent interest rate, after a few years that account is going to look great. You just have to refrain from drawing on that account as much as you can.

Clearing your debt so you can invest more

Now that I’ve explained the two types of interest you can see how the creditors are making there money. You can also see why it is certainly to your benefit to get out of those high interest loans.

I’m not going to focus on this too much in this particular blog as I have blogged about debts previously about how to get out of debt quickly. Simply put it’s best to pay off high interest rate loans first, and as you pay them off add the amount you were paying to one creditor to another debt and it will have a snowball effect.

 

 

Wrapping things up

I bet you may be scratching your head too, it is a rather complicated system for calculating interest rates. I can assure you there are much more complicated formulas out there, and I’m not even going to attempt them.

I just felt like this information is something that may help my readers learn to save money and get themselves out of debt.

We are all looking to get out of the rat race, unless of course you’ve already gotten out, than great for you! Wouldn’t it be nice to just be able to decide suddenly that you want o take a trip overseas to someplace you have never been? I know that I would love to visit many places abroad, but I just have to nail down that financial stability.

I’ll bet that if you are visiting my site and reading my blogs I would venture to take a guess that you are in a similar boat financially, or you’re really bored, haha. If you’re bored than thank you for visiting my site.

The formulas I used here as well as the table showing how compound interest were all from TheCalculatorSite.com.

Anyway, I hope that you found some information that I provided here useful in some way or another. If you have any questions, comments, or concerns as always please feel free to comment below or email me directly. I try to respond to emails within a day.

All my best to you and yours,

Matt

 

*Disclaimer – I am not a certified Financial Adviser, Accountant, nor am I an Attorney, So any advice given in my blogs is solely based on my opinions.*

 

5 thoughts on “Difference between simple and compound interest

  1. Math was never my strong point it was more reading time that got me excited. What you are sharing is pretty amazing and will an can help those like myself. Your post is very informative with a lot of good information. Thanks again for an awesome post.

    1. Thank you Norman, I appreciate the kind words. I know this was a tough lesson for me to learn, but now that I know it will continue to help me in the future.

  2. Hi Matt. This is awesome information, I’ve never really looked into what compound interest was before. I’m from Australia and I’m embarrassed to admit it but I’ve gotten myself into some terrible credit card debt. I ended up with a $10,00 debt and I hate to think of the interest I would have paid had I not paid it off quickly. I got so sick and tired of paying off the minimum that I started paying it off in big chunks by working long hours of overtime, which I’m so glad I did. I cringe when I think of what I potentially could have been charged in interest if I had just kept my minimum repayments. What kind of interest is charged to credit card debt? Is that compound or simple?

  3. Thanks for the “math class” Matt. Thanks for the comprehensive explanation as regards to compound interest and simple interest (usually involving our bills / debts).

    In fact, I did use my “scientific calculator” to calculate the figures. Thanks for the informative post!

    Albert Einstein described “compound interest” as the 8th MARVEL OF THE WORLD. That’s why people who focus on creating passive income / assets are FILTHY RICH.

    -ChrisC.

    1. He was absolutely right to say that too. I appreciate you taking the time to read my blog. It really is amazing how compound interest works. Thank you again for taking the time to write back.

      Best to all you and yours,

      Matt

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