So when does a compound loan equal a simple interest loan?

Let’s say you borrow $150,000 and can afford a $1300 a month payment. The simple interest loan is 4%. The compound interest rate must be greater than 6.797644% or you’ll end up paying the same amount of interest and pay off the loans in the same amount of time. So a compound interest rate has to be nearly 2.8% higher than the simple interest loan or you’ll save money with the compound interest loan even though it has a higher interest rate.

If you can afford $1500 a month the compound rate has to be 6.959813% or higher or you’re better off with a compound interest loan.

Let’s try $1000 a month. Now the compound rate has to be 6.3629203% or higher or it’s a better deal than a 4% simple interest loan.

What you can see is that a simple interest loan is about equivelent to a compound interest loan that has an interest rate 2%-3% higher.

One of the claims of a simple interest loan is that you can pay it off in half the time without changing your payment. Let’s stick with a 4% simple interest loan on a $150,000 mortgage with a $1300 payment. It’s going to take about 188 months to pay off the simple interest loan. The interest on your compound interest loan would have to be more than 9.8% for that to be a true statement.

If we dropped the interest rate on the compound interest rate loan to 4% you’d pay it off in 146 months. More than 3 years earlier than the simple interest loan with the same rate.

We can see from this that it’s very difficult for a simple interest loan to save you money over a compound interest loan.

One last thing to consider is how much money you save in interest by increasing your monthly payment. We’ll start with a $1000 a month payment on a 150,000 loan. The interest rate for the simple interest is 4% and the interest rate for the compound interest is about 6.36% so both loans at $1000 a month cost you 150,000 in interest. Now let’s raise the payment $100.

You save $25,000 of simple interest. You save $33,000 in compound interest and pay off the loan 7 months earlier.

So you can see that putting extra money on a compound interest loan has a greater effect than putting extra money on a simple interest loan.

So you can see that unless you get a ridiculously low interest rate on a simple interest loan, it is very difficult to save money over a compound interest loan.

In this part I’ll demonstrate how people use bad math to convince you that a simple interest loan is better.

Let’s say I put $1000 into a bank account with a 7% interest rate. One bank account pays 7% in simple interest and the other pays 7% in compound interest. Compounded monthly.

As you can see you’re going to have significantly more money after 30 years with compound interest. Now, imagine you would owe that money rather than recieve that money. Obviously you’d rather owe the $2000 accumulated through simple interest than the $7000 accumulated through compound interest, right? Obviously you want to owe less so using the “savings” example to illustrate the “loan” you can be tricked into thinking simple interest is better.

But since you read the previous two posts you know something is not right. The “savings” example is not relavent to loans. The reason isn’t entirely obvious. It’s because when you’re saving money the principle balance is increasing where when you pay back a loan the principle balance is decreasing.

If you want to compare the savings example to a loan example, flip the chart vertically. Now it looks like the charts you saw in the last post. The red line starts at the same point as the blue line but goes down progressively faster.

By reducing the amount of principle in a compound interest loan you reduce the amount of interest owed the next month and the next month, etc until the loan is paid off. In a simple interest loan you never reduce the amount of interest owed. In order to progressively put more money towards principle in a simple interest loan you have to progressively increase your monthly payment. In order to progressively put more money towards principle in a compound interest loan you can maintain a monthly payment that has a non zero amount applied to principle at the beginning.

So now you know why you may have been tempted by a simple interest loan so you can tell the insurance (or mortgage) agent why his presentation is misleading.

The only time a simple interest loan is worth it is if the interest on the simple interest loan is significantly less than any compound interest loan you could get. If you can only get a 7% rate for a conventional mortgage but someone is willing to give you a 4% simple interest rate loan, then it may save you money.

But do the math before you sign any papers. You can see how easy it is to be fooled if you don’t.

In part 1 I gave an example that demonstrates why you should never get a simple interest rate loan. In this part I will show you pictures to illustrate the point and provide an excel file that has all the calculations.

The above chart shows the amount of interest paid for a simple interest loan and a compound interest loan at 7%. The loan is for $150,000. The payment is $1500 per month. The red area is the total compound interest paid. The blue area is the total simple interest paid. Notice that it includes the compound interest. With the simple interest the loan is paid off in 240 months or 20 years. With the compound interest it’s paid off in about 12 and a half years.

This chart shows you the remaining balance over time. You can see that the compound interest loan is paid off a lot quicker and saves a lot of money in interest.

This is the excel sheet with all the calculations: simple-vs-compound-interest

In the first month both loans cost $875 in interest. In the second month the simple interest loan still costs $875 in interest but the compound interest is down to $871.35 in interest.

This should make it even more obvious why you should never get a simple interest loan. A simple interest loan always costs far more money than a comparable compound interest loan.

To calculate your monthly payment for a simple interest loan take the daily rate times the number of years to pay it off times 365. Add the amount of the loan. Divide by the number of years you intend to pay it off in. Divide by 12. To calculate the monthly payment for a compound interest loan use BankRate.com.

Compare.

I recently had a life insurance sales person come by go through a whole presentation on saving money. Part of the presentation was a sample person paying something like 7% for a conventional home loan. He then showed how the person was able to pay the house off in half the time with a simple interest rate loan at 4%. The obvious problem with this scenario is the different interest rate. Obviously if you drop the interest rate significantly you’re going to save a lot of money per month or be able to pay your house off faster.

Let’s say I have a $150,000 mortgage at 7%. With a conventional loan (which uses compound interest) the monthly payment is $997.95. If I get a 4% interest rate the payment goes down to $716.12. A savings of over $280 dollars per month. Now, let’s pay off that 4% loan with the 7% payment. The loan will be paid off in 17 and a half years instead of 30. Total interest paid is $54,580.

Now, let’s switch to a simple interest loan at 4%. 4% of $150,000 is $6000 of interest. Banks calculate the daily interest for simple interest by dividing the yearly interest by 360. So the daily interest is $16.67. The simple interest daily rate never changes so the math is very simple. We want to pay off our loan in 17 and a half years. That’s 365*17 + 365/2 days or about 6387 days. Which is about $106,471 worth of interest. That’s nearly twice the amount of interest we would have paid had we gotten a conventional loan with a 4% interest rate.

Our original loan at 7% for 30 years would have cost over $209,000 in interest. So the simple interest loan at 4% cuts the interest nearly in half. But now let’s see what our payment would be on a simple interest loan that we pay off as quickly as we could pay off a 4% conventional loan.

We have $106,471 in interest to play plus the $150,000. So in total we have to pay $256,471 off in 17 and a half years. That requires a payment of $1221.29 a month. More than $200 more than our original payment. And nearly $500 more per month than a compound interest loan at 4%.

Compared to a 7% 30 year conventional loan the 4% simple interest loan looks like a great deal. The only way a simple interest loan saves you money is by having a much lower interest rate and having a much lower pay off time. And no matter what, a comparable compound interest loan will beat a simple interest loan by a significant amount.

So in conclusion, if someone tries to sell you a simple interest rate loan, make them compare it to a compound interest rate loan with the same interest rate. Then tell them to get lost.

If you’re looking to invest this would be a good time to do it. Many stocks are on sale as a result of a massive plunge today. The upside to all of this is that oil is now less than $90 a barrel. While advertisers still try to play on “rising gas prices” to sell you various things the fact is that gas prices have been going down. People expected the hurricanes to drive up gas prices and yet they continued downward. Only in areas directly affected by the hurricanes did gas prices go up. And much of that was due to price gouging and media driven panic.

That should be a big giant clue that oil prices are highly inflated and are not related to current supply vs demand. If that were the issue then refineries in the gulf going out of commission would have affected gas prices in Arizona. But it didn’t. Gas prices continued their downward trend inching closer to $3.00 a gallon.

Oil prices are related to the market which is based on emotions and speculation. So since the market is tanking so are oil prices.

I’m currently invested in a Candian Royality Trust which has its hands in every aspect of the oil industry in Canada. The stock is worth about half of what I paid for it although generous dividends have limited the actual loss.

How low can the markets go? Who knows. But it will bounce back. So you can wait for it to bottom out or start buying discount stock now. I’d start buying discount stock now. If the stock continues to drop then buy more of it. Eventually it will go back up and you have a very good chance of coming out ahead.

You just have to make sure you’re investing in good companies going through a rough time. And not bad companies that will end up going bankrupt. There’s nothing less fun than seeing a stock you heavily invested in suddenly not being on the exchange.