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# Compound Interest

Sunday 23 December 2018

So! I have been meaning to post something about this for a while. Please let me start with a disclaimer - I am only passing on what I have heard at workshops and am open to being corrected in the comments!  In the unit on compound interest, the IB syllabus requires that students adjust the interest rate based on the compounding period. If, for example, a bank offers 4% pa compounded quarterly, then students would be expected to divide the interest rate by 12 (so it is a monthly interest rate) and then multiply the number of years by twelve to get to the number of compounding periods. Logical enough right? Well, apprently, that depends on where you are from. A couple of workshop participants fro, Denmark (and possibly others from Norway or Sweden) have enlightened me to the fact that where they are from, if a bank quoates an interest rate of 4%pa, this already considers that interest is being calculated twelve times a year. As such, the monthly interest rate is what ever it needs to be so that the investment will be 4% bigger at the end of the year. Effectively 4% simple interest on the year, provided no funds are addedd or taken away in between......

As required by the IB syllabus....

$$100\times { \left( 1+\frac { \frac { 4 }{ 12 } }{ 100 } \right) }^{ 12 }=\quad 104.07\quad (2dp)\\ An\quad increase\quad of\quad just\quad under\quad 4.1%\\ \\ Solving\quad the\quad following\quad equation\\ 100\times { \left( 1+\frac { \frac { r }{ 12 } }{ 100 } \right) }^{ 12 }=104,\quad gives\\ r=3.93\quad (2dp)$$

Now consdiering the Danish model....

$$Solving\quad the\quad following\quad equation\\ 100\times { \left( 1+\frac { \frac { r }{ 12 } }{ 100 } \right) }^{ 12 }=104,\quad gives\\ r=3.93\quad (2dp)$$

Now I never knew that! Interesting no? Please correct me or comment,

Thanks, Jim