Compounding monthly grade 11 | Financial Maths #Finance

this CashNews.co is about a person who invests a particular amount of money but the place where he’s investing the money gives him three different investment options and what we are going to do is work out how much interest he will earn for the three different options in order to help

him decide which investment is going to be best option number one says that Johan will invest five thousand Rand at nine percent per annum simple interest determine how much money he will have after two years so remember simple interest uses the formula as shown over there where P will be his

starting amount which is five thousand rent the interest rate is nine percent per year so that’s just going to be nine over a hundred times by the number of years which is 2. if you had to go do that you would get an answer of five thousand nine hundred Rand so that’s how much your hand

would have if you chose that investment so I’m just going to say here five thousand nine hundred Rand option number two he could invest it also at nine percent but using compound interest so now we just modify our formula and if you guys do understand the difference between compound interest

and simple you would already know which investment option will be the best out of those two nonetheless we use the compound interest formula and let’s see what we get so it’s going to be nine percent so I’m going to say nine over a hundred and then the years will be the exponent

on the outside and that gives us an answer of 5940 Rand and 50 cents so there we can see that compound interest will always beat simple interest because yup there’s a CashNews.co that I’ve done which explains the difference between compound and simple but compound interest always wins

because when you do compound interest you keep updating the amount in fact let’s have a look at that now because it’s going to help us when we look at option three because in option three it’s something new that we’re going to talk about so with option two let’s have a

look at that quickly so there’s this guy honey starts off with five thousand Rand and for the first year he’s going to earn nine percent okay so nine percent of five thousand is 450 Rand so after one year Johan will have five thousand four hundred and fifty Rand going into year number

two he now has 5450 so we’re gonna take nine percent of five thousand four hundred and fifty Rand which is 490 Rand and 50 cents and so if we add that to his 5450 Rand with this we then see how he got the final or how we got the final amount of five thousand nine hundred and forty Rand and 50

cents so how often did we update his amount well we did it every year and that is what compounding per year actually means in option number three we are going to update the amount every single month okay so now things are going to work a little bit differently so the formula is going to be modified

slightly so the formula usually looks like this but what I want you guys to think about is the formula rather looking like this and this is something new for grade 11. so let’s do something like this I’m just gonna your teacher might use a different letter I’m just going to use

the W so what w means you must always remember this it’s the number of times that you compound in one year so if you have an investment that is compounded yearly well then that means it’s going to compound every year so it will be once per year and that’s what we’ve been

doing up till now where this number has just been a one and so that’s why I haven’t really mentioned it I’ve ignored it but if you compound monthly then how many times does that mean per year well that means 12 times right so that means we’re going to put a 12 over there and

now this number here is the total number of compoundings so imagine this your money gets compounded every single month and you’re investing for two years that means it’s going to compound 24 times in total and so the new formula or the new structure will be like this it was a nine

percent interest rate so that’s nine over a hundred like that and then I’m just gonna put the little W next to it which is times 12. to the power of 24. and if you do all of that on the calculator you’re going to get a final answer of 5982 Rand and then it’s going to be 0.07

cents okay so notice this your Han is going to earn slightly more when he invests so let me just fold that value in 5 9 8 2.07 he earned slightly more for option three because they are updating his amount more often so imagine this for option number two they’re gonna update his amount they or

they’re gonna they’re gonna update every year so let’s say he starts investing in 2015 for example okay that means that all the way until 2000 and not around all the way until 2016 they are going to be basing that nine percent off of his initial amount of 5 000 Rand only after

that first year is complete and then they will upgrade his amount or they’ll change it they’ll see how much he has at the end of 2015 and then they’ll upgrade that going into the next year however when you compound monthly they’re gonna do this let’s say you start on

the 1st of January on the 1st of February they’re gonna say okay stop let’s see how much money he actually has he would probably have a little bit more than five thousand Rand so let’s say he has five thousand and fifty red they then say oh okay well now we need to change it to

nine percent using that amount then the first of March arrives and they say okay let’s see how much he has now so you see that they updating the amount more often and so the money is able to grow faster instead of waiting for a whole year before they update with simple interest which is

option one they never update they take the initial 5000 and they just keep using that the whole time I hope that makes sense so the main thing to take away from this CashNews.co is the more often you compound the more faster the money can grow and that the compound interest formula this W once

again it’s my own letter your teacher will use something different it doesn’t really matter what does matter is that that value there is the number of times that you compound in one year and then this number here should be the total number of times that you compound for the whole

investment