The power of compounding interest

January 4, 2011 by Kenneth O'Connor

3 comments

It is said that when Albert Einstein was asked what the most powerful force in the universe was he simply replied “compound interest.” This coming from the guy who developed the general theory of relativity, along with 300 published scientific works. I was humbled by the thought, regardless if Einstein actually said this or not because compound interest is indeed powerful enough to affect the lives of every person on Earth. Perhaps it took a name like Albert Einstein to remind us how critical this topic is.

So what is the most powerful force in the universe?

However, much to my dismay, many people actively participate in agreements and make financial plans for their life without understanding what compound interest really means. I am talking about car loans, retirement plans, mortgages, student loans, annuities and many other financially based products that play a role in our lives everyday. The resulting financial decisions end up negatively affecting quality of life either now, or in the future of that person. By learning about the power of compounding interest a person can learn to make better decisions about their money and their responsibilities. College students can especially benefit from mastering this concept because they can avoid financial entanglements early and set themselves up for success in the future.

So what is “interest”? – Interest is the cost associated with borrowing or lending money. It can be considered a fee on borrowed assets. When lending money, banks apply an interest rate to the loan so that the amount repaid is greater than what was originally lent, creating a profit. A loan will have an annual percentage rate (APR) to explain the interest cost of this loan in one year.

Generally, it is the interest rate of a loan that determines the total cost to the consumer. A high interest rate loan will cost more to repay than a low interest rate loan, all things being equal. Therefore it behooves borrowers to search for a loan with a low rate in order to reduce the costs of repayment. Here is an example to compare.

Bobby borrows $10,000 with an APR of 5 percent. The loan begins repayment immediately with a 10 year monthly payment schedule of $106.07. At the end of 10 years, Bobby pays back $12,727.70. The additional $2,727.70 paid to the bank is the bank’s “profit” from providing the loan.

Annie borrows $10,000 with an APR of 10 percent. The loan begins repayment immediately with a 10 year monthly payment schedule of $132.15. At the end of 10 years, Annie pays back $15,858.15. The additional $5,858.15 paid to the bank is considered the “profit”.

The interest rate for Annie was twice what Bobby had but Annie ended up repaying more than twice the interest cost of Bobby.

So what about “Compounding Interest?” – Compounding interest is when any interest accrued on a loan is added to the outstanding principal amount borrowed. This amount added to the principal begins to accrue interest immediately.

Consider an example of a bank account with interest compounded every year at 20%. An account with $1000 initial principal would have a balance of $1200 at the end of the first year. In the following year, that $1200 would grow another 20% to $1440. In the third year $1440 would grow to $1,728 and so on.

Taking control of compounding interest – Many people have their first encounter with compounding interest when using credit cards. The debts on a credit card can quickly stack up if not paid off quickly and aggressively. The same thing holds true with student loans. The interest rate on student loans is typically lower than a credit card, but the volume of money borrowed for student loans means that debts can add up quickly as well. It is recommended to follow aggressive repayment of student loans to eliminate the debt quickly. The following three examples are of student loan repayment plans for your comparison. Please note the major differences of cost.

Paul A. borrows a private student loan for $10,000 for each of his four years of college. They each have a 7% rate. Paul elects to not make any payments towards this loan until after graduation. Upon graduation, the loans enter repayment with a total outstanding balance of $44,399.43. This will require a monthly payment of $515.52 every month for the next 10 years to complete repayment. The total amount repaid is $61,862.40.

Ryan B. borrows a private student loan for $10,000 for each of his four years of college. They each have a 7% rate. Ryan elects to begin loan repayment while in school. As soon as the loan disburses he begins making payments of $116.11 a month. Upon graduation the total outstanding loan debt is $39,912.85. This will require a monthly payment of $463.42 for the next 10 years to complete repayment. The total amount repaid is $55,610.65.

Rob C. borrows a private student loan for $10,000 for each of his four years of college. They each have a 7% rate. Ryan pays $116.11 plus an additional $100 for a total monthly payment of $216.11. Upon graduation the total outstanding debt is $35,849.02. This will require monthly payments of $416.24 over the next ten years to complete repayment. The total amount repaid is $49,948.50.

The Phrase that pays – The above examples lead to one conclusion; “Pay a little now and save a lot later”. Each one of the examples has the exact same loan amount and interest rate and period of repayment. The only thing that is different is the repayment schedule each student follows. Because Paul A. decides not to make any payments towards his loans while in school, it ends up costing much more to repay in the long run. That is a direct result of the power of compounding interest further increasing debts left unchecked. Because Ryan B. makes payments while in school, his loan costs $6251.90 less to repay than Paul. Rob C’s aggressive repayment plan saves him $11,913.90 over the original cost of the loan and puts him in the best position for debt freedom. If Rob continued to accelerate his repayment he could get out of debt even faster.

In each one of these scenarios, the power of compounding interest was in place to allow for debts to increase. It was the reaction of each of these students that dictated the outcome of repayment. By getting pro-active with repayment, a borrower can mitigate the expansion of debt to an unmanageable amount. If a student chooses not to make payments while in school, they should recognize that compound interest will force that debt to increase and cost much for repayment later. The wise move is to counter the impact of compounding interest by beginning loan repayment immediately, and adding additional accelerating payments if possible.

Getting compound interest to work for you – The true power of compound interest is found in simplicity and applicability; Simplicity, because of the basic nature of the concept and applicability because of the many people that partake in its use everyday. However for the most part, interaction with compounding interest only comes in situations where we owe debt like for houses, cars and school. The great thing is getting compounding interest to work for you. This is where the power of saving money is so important. In Rob C’s example he was able to save $11,913.90 from loan interest payments. If Rob C. saves this money at an average annual return of 7% he would have $23,942.96 at the end of 10 years.

In this economy, every dollar counts. Your goal should be to eliminate debt as quickly as possible and build personal savings to harness the power of compounding interest for yourself. Letting debts grow out of control early is a sure way to eliminate wealth building in the future.

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  • April

    This article helped me understand more about student loans and compounding interest than any government website.

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    I was wondering where I could find info on this. The power of compounding interest saved me a lot of time. Please, keep it up!

  • Grant

    I just stumbled on this article when I was looking for some stuff on my loans from Wells Fargo. I know this is old but your article has a ton of errors in it. First, private student loan interest isn’t always capitalized during the loan. Wells Fargo for instance doesn’t capitalize until you start making payments after college. For example I took out a loan for 10k on 1/02/09 at 6.44%, on 3/31/11 the outstanding was 10k plus 1432.70. So give or take the interest rate for 2.25 years would be 14.49% but that makes sense given there are fewer days in the first quarter of the year so its a little high. With just simple compounding I would be over 1500 in interest. Stafford unsubsidized however does do this.

    This brings me to my next point interest compounding is huge when you are talking about retirement and investments compounding over 30-40 years. However, when you are talking about over the course of college well its not. Because its not even 4 years of compounding 40k its 1 year of compounding of 40k, 2 on 30k, 3 on 20k and 1 on 10k. So using your example which I’m not quite sure how you got your numbers; For simple interest (10k times 28%)+ (10k time 21%) + (10k times 14%) + (10k times + 7%) = 47000, even with doing semester disbursements I’m getting only 46300. Using a compound interest calculator, compounded daily at 7 percent yr1 would end with (10725.01), yr2 (22,227.59), y3 (34564.12), y4 (47,795). So we are really only talking about a 795 dollar difference between compound and non-compound anyways which is a measly .4% a year. I however didn’t take into effect that the last year really isn’t a year its more like 9 months until they are capitalized to a full loan but that’s pretty irrelevant.

    This brings me to your point that the individual who didn’t pay through college paid more because of “compound interest”. Well this isn’t true. They paid more because they had a higher principal, post. grad. causing them to have to pay more based on the amortization schedule. Given the compound interest was only $795 dollars after 4 years compared to simple interest that obviously wasn’t the cause of a 5k to 12k gap between students. But that is irrelevant anyways because your numbers are wrong again. Paul will pay close to 62000, Ryan will pay 55,600 and Rob will pay 50000, however this is POST graduation, you can’t ignore the pre-graduation payments which means Ryan really paid 55600+5600 = 61200 and Rob really paid 50000+10400 = 60,400. So yes they are still saving money, but not nearly what you are claiming they are saving. Rob never saved that much much as you claim because he fronted the cost which you completely left out of your analysis. If two people walk into a car dealership and buy the same car for the same price, but one puts a 10k cash down payment on it that doesn’t mean that person go the car for 10k cheaper. That’s absurd, but its what you explained for college loans repayment.

    Before I get to my last point, I’m not sure if you even understand what compound interest is. A quote from the last paragraph “However for the most part, interaction with compounding interest only comes in situations where we owe debt like for houses, cars and school”. School I have already address, lets talk about a house and a car for a minute neither of them if you are making regular payments will every encounter a compound interest situation. You are confusing compound interest with an amortization schedule. Every month you make a payment on a car or a house, the interest on those objects is back to zero, but in addition to the interest, you are paying some principal, hence why the next month you pay less interest and more principal until the loan is paid off the only way you would ever see compound interest on a house is with one of those funky loans they were doing during the housing bubble that each month your payment was less than the actual amount of the amortization schedule increasing the principal not decreasing it. You also mentioned credit cards as an example which is also wrong, federal law prohibits credit cards from allowing payments less than the interest on the card, there has to be a payoff date and it has to show you on your statement what that will be if the minimum balance is paid each month.

    Which brings me to my final point, your analysis stopped one step short and assumed they should be paying back 1400 or 2600 and didn’t look at opportunity cost. If you take this one step further, I would assume the individual is working to pay off these loans which means he has earned income which allows him to open a Roth IRA while in undergrad. Lets say they Paul told his two buddies they were crazy and invested the 216 a month into his Roth at 7 percent a year, which is lower than the annualized return of the market but is reasonable. Paul would have close to 11900 at graduation. Well obviously Ryan and Rob are laughing at him because he has more money but still has those pesky student loans. Paul however chuckles to himself and moves on.

    So Ryan and Rob say well I’m going to invest that extra amount I’m saving each month on my loan in my Roth account. Poor guys though now that they are graduated and earning a good salary they are going to have to pay taxes before they put it in their account unlike Paul since he never made enough income in college to owe taxes, but we’ll ignore that part for simplicity. So Ryan invests his extra 50 a month and Rob invests his extra 100 for next 10 years but because Paul is trying to pay off that loan so he doesn’t invest anything so at 32 years old everyone is debt free and for whatever reason they all stop investing and Ryan has approx 8700, Rob has 17300 and Paul has 24000. But like with college compounding these numbers are just as irreverent its too short of a time period Rob still wins. Lets fast forward to 65 and they are retiring. However now we have another 32 years of compounding, so who really made the best choice.

    Ryan : 87,600 – 55600 – 5600 = $26400
    Rob : 174,250 – 50000 – 10368 = $113850
    Paul : 241,700 – 62000 = $179700

    THAT is the power of compounding and that is what every high school, college, and university should be teaching. It shouldn’t be student loans are scary, because the post grad payback payment, which you showed perfectly is only a 50 dollar difference each month in your example. That’s not eating out once or twice a month no big deal. This analysis should be done with every person that walks into a student loan office and says I don’t know how much money I need, but I am going to be working some. Because if someone walked into your office and you gave them the advice from this column you just cost them somewhere between 65k and 150k with a very conservative return of 7 percent on the stock market.

    I would suggest taking another look at the article and fixing it given that people can still find it and you are misleading them with you analysis.

    Grant