Financial maths grade 11 | Compound Quarterly and Semi Annually #Finance

in this CashNews.co we’re going to look at all the different kinds of ways that money can be compounded up till now we’ve only looked at what we’ve typically only looked at compound yearly but money can be compounded monthly daily semi-annually quarterly but that’ll

all become more clear as we proceed through this CashNews.co so here we have a guy called kariso and he starts an investment with a deposit of 20 000 Rand then the interest rate that this financial institution offers well that’s going to change for the first two years it says here year one

and year two it’ll be seven percent per annum uh I should actually just fix it up quickly yeah just added compound interest there just so that people don’t feel it might be simple interest you’re three and four eight percent compounded monthly you’re five and then year six

so it’s a six year investment let’s see how that works so remember one of the CashNews.cos on a guy called vusi we showed that when their interest rate changes you can simply add all the brackets next to each other I’m just going to remind you about that quickly so let’s

just look at your one and year two for now we know that we can just use this formula it’s compounded yearly if they don’t mention anything else so we can just say he starts off with 20 000 Rand and he’s going to earn seven percent now in the previous CashNews.cos I would often say

seven over a hundred but I’m going to start doing it in a slightly different way I’m going to write out 7 over 100 is 0.07 so I’m just going to write it like that from now on it’s more comfortable for me and that’s for two years okay and that would give Lucy no no this

question is that’s going to give him a total of nice round number 22 898 so this is how much krissa will have after two years what interest rate would he then use well it tells us that is in year three and four so for the next two years it’s going to be compounded monthly okay so

we’re going to use the same formula but remember we said that if it’s not yearly we should upgrade it with this little value over here where this number here is the amount of times that it compounds in a year so if you compounding every single month that means you’re doing a 12

times per year so going into the next two years what’s the starting amount well it’s not 20 000 anymore because he’s it’s grown up to twenty two thousand eight hundred and ninety eight and the interest rate is now going to be eight percent which is the same as 0.08 divided

by it’s going to compound 12 times per year for a total of 24 times because it’s year 3 and year 4 so that’s year three will be 12 and year four will be 12 so that’s 24 times in total and let’s see what that gives them and yes I am doing this the slow way some of you

at home might be thinking why I’m doing it the slow way I’m just trying to I’m going to show you the fast way as well I’m just trying to make sure everybody understands and that gives a total value of 26 856.787 I’m just going to put the first three decimal places on

the calculator because that’s not the final answer okay so now going into year five they’re gonna change the interest rate to nine percent compounded quarterly that means every quarter of the year so that means four times per year so I’m gonna do that here I’m going to use

the same formula where he now has 26 856.787 1 plus the interest rate is nine percent so that’s 0.09 four times per year and how many years will the interest rate be like this well it’s only for year five so it’s only for one year so how many times will it compound in that one

year well that’s also going to be four times and if you work that out you’re going to get a value of 29 356.705 and then for year six they’re going to go at seven percent compounded semi-annually annually means per year so semi-urly means every six months right so how many times

will that be in one year well that’s twice so we can use the same formula again where karito now has 29 356.705 1 plus it’s going to be 0.07 two times in that year and how many years will the interest rate be like that well only for two years I mean only for one year so how many times

is it going to compound in cheer well that’s twice but because it’s only because that interest rate is only going to be valid for one year then it means this number here will also be a two okay and if you go work that out your final answer is going to be 31 447.64 Rand now that was the

slightly longer way this uh what I’m going to show you next is very quick remember the question on or the CashNews.co that we did with vusi we said that if the interest rate changes instead of calculating your value each time you can just do it in one step like this so he starts off with 20

000 Rand and the first interest is seven percent uh that’s yearly so we can put a little one there if you want to it doesn’t really matter and that was for two years then instead of getting this answer and then using it for the next part so you know we would in the next part we would

have used this formula again and you would have taken this answer and you would have used that over there right so instead of working this out let’s just leave it like the way it is so we don’t it just works out a lot faster so all we do now is we just open up the next bracket and we

say one plus and now we’re looking at year three and four which is eight percent compounded monthly so that means there’s a 24 there because it’s 12 times per year which is 24 times if it’s for two years then instead of working anything out we just open up the next bracket

which is going into year five and that’s nine percent compounded quarterly so you just do this and for how many years are we going to compound quarterly or only one year so that means we’ll put a four there as well and then the last part is seven percent semi-annually and that’s

also only going to be for one year so we’ll just put a little two there because if you’re compounding for one year it means you’re going to compound a total of two times in that year if it’s compounding semi-annually then you can take that and put all of that on the

calculator in one step and you’ll still get the same answer