Posted by Eduardo (OR) on June 14, 1999 at 20:43:40:
Hi John–
Thought you might like this one. As you know, simple interest loans have interest computed entirely on the original principal. Compound interest is based on a principal that is increased each time interest is earned. So, compound interest results in the larger return–following the first time interest is earned. But not before! For example, a loan is set up at compound interest: $1,000 at 10% per annum compounded annually. But the loan is paid at the end of six months. What is the interest paid? $48.81 (use c status indicator with the HP-12C). The same loan at simple interest gives the result: $50.00. (I like to visualize compounding returns being along a curved line and simple interest computing being along a straight line. Where the lines cross is where compound and simple pay the same amount [at the end of one year in the example]. Before they cross [before the first time interest is earned], the line for compounding dips below the straight line for simple and here, then, simple interest always pays more.) Just a little interesting tidbit. Enjoy your posts. --Eduardo
Simple interest vs. compound interest - Posted by John Behle
Posted by John Behle on June 08, 1999 at 21:09:26:
Many people are so used to entering monthly compounding periods that they try to do it with balloon payments too.
Example: 10,0000 note 10% interest - due in 5 years
There are no monthly payments.
How much is the balloon payment? $16,453.09 or $16,105.10? Which do you get? Which is right?
The first figure is based on interest compounding monthly. Instead of 10% per year, it is .83% per month compounding each month. The second figure is based on an annual rate of 10% compounding once per year. The second figure is correct, though even banks, mortgage companies and title companies have to be corrected on this one occasionally.
Discounting is the same way. Let’s take the real figure of $16,105.10 and discount it to a 15% yield. What would you pay for the note? $8,007.08 or $7,642.96? Which is correct? The first is based on entering 15% annual yield into the calculator and 5 years. The second figure is based on entering 1.25% periodic rate and figuring 60 months.
Just as monthly compounding ends up in a larger accrual of interest, monthly discounting ends up telling you to pay less for the note. If you want a true 15% yield on this note, you pay the first or higher figure. The second figure is not 15% - it is 1.25% per month compounded. The actual rate on the second calculation is 16.08%, though most people in the industry will think it is 15%. That’s fine - I just like to know my true yield.
Thanks John! I knew your posts were worth reading, even if over my head.
For a few months I have been trying to figure out how to calculate the interest rate on $11,000 borrowed for 2 years, no payments, and pay back is $15,000. A friend figured it out using a spreadsheet but I HAD to learn to do it on an HP 10B (without just asking for the answer on this forum. I mean, if I’m going to be a rich investor I’d better learn this for myself.)
Your post above pointed out my flaw - my calculator was set to 12 payments per year instead of 1.
After resetting it - MAGIC! I get the answer and find out Mom gets repaid 16.775% (which I will rub-in how much better I pay than her bank!)
I feel like I just graduated from elementary school to junior high!