Financial maths grade 11: Exam #Finance

this is a obviously as you guys can probably see immediately this is a financial maths question um but grade 12 so you guys must remember that not every single grade 12 I mean not every Financial maths question that you are gonna get is necessarily gonna be a grade 12 type of question what

I noticed is that a lot of Learners in grade 12 they only ever want to use the F or the P formula the future value or the present form present value formula but guys this question as we are going to see now is not a grade 12 question this is actually a grade 11 type of question all right they can

definitely ask you something like this so let’s see how it goes seven marks that’s quite decent right so yeah we’ve got someone babalua never heard a name like that before babalua um has three sons she would like to give each of them sixty thousand Rand at the end of the year in

which they turn 18. okay case that’s a lovely Mom I wish I mean these I would love to have gotten sixty thousand round when I turned 18. um she plans to invest a single lump sum into a fund on the 1st of January 2015. um the fund is going to earn interest blah blah blah blah blah after that

it will earn interest like that and like that and like that and then on the 1st of January 2015 her sons will be eight years old 11 years old and 14 years old calculate the value of the deposit now I can I can imagine that a lot of you reading this you are like what this looks terrible but I can

assure you that this is not actually that bad at all so what I’m gonna do is I’m going to draw us a timeline so this is a grade 11 type stuff okay so we’re going to draw a timeline and I actually like to draw two timelines why because I’m cool like that um when your teacher

does one timeline I’m I’m way cooler remember so I do too now I’m just joking guys I just like to do uh two timelines okay the one timeline is for all of the money like the deposits and the withdrawals and then the other timeline I used that one just for the different

Interest Rates I don’t like to put it all on one timeline because it just makes it look a little bit uh messy or crammed um so what we’re going to do is I’m gonna just put all the different deposits and things like that so let’s see okay so what this lady is

gonna do so I want you to imagine that you are babalua okay and you would like to invest money so you are gonna put money into an account now we don’t know how much money you are going to put into the account in the very beginning so let’s just say that that will be X we don’t

know how much money that’s going to be so we’ll just say X okay then when each of her children turn 18 years old she’s gonna take 60 000 Rand out so that she can give it to them does that make sense so we need to try to understand when that will be so this lady has three children

there’s an eight-year-old 11 year old and a 14 year old who is gonna reach 18 years old first well the 14 year old of course how long will it take until the 14 year old becomes 18 well that would be um four years so in four years time babalua is going to take 60 000 Rand out of her account so

that she can give it to her first child then um how Okay so so you gotta you got to think about this carefully um this would take seven years right for this kid to reach 18 so that would take seven years so that would be a t7 she’s gonna give out another sixty thousand Rand okay and then how

long is the youngest one going to take to reach 18 well that would take the youngest one 10 years and so that would be the end of our question so I’m just going to put a T10 over here um actually let me make my number line a little bit shorter doesn’t need to be that long so maybe we

can just go up to there and then the interest rate timeline we can just do up to there so at T10 she’s gonna give out her last 60 000 rent and that’s it that is how this question is set up now what I like to go and do is I’ll then go look at the interest rate so it says that the

fund will earn an interest rate of 7.9 percent compounded monthly for the first four years okay so up to T4 the interest rate is going to be 7.9 percent and that’s monthly all right then it changes to 10.5 percent compounded half yearly so that’s some of you might like to call that

semi-annually okay so that’s going to be 10.5 uh percent half yearly and that’s all the way up to T10 all right so that’s the difficult part to be honest so guys the way that it works is the following the way that I handle Financial maths questions is the following for grade 11

specifically so what I do is I I look on the green timeline the timeline that has all these different these different amounts and I start with the first one okay I’ll start with the first one and I I completely ignore the other ones I just ignore them I’m only looking at the first one

which is X and what I’m going to do with that X is I’m gonna compound it all the way to the end all the way till T10 okay so what would that look like well that would look like this uh let me try and make this nice and easy for you guys um I’m gonna do something quickly some

students like it if I do this I’m going to write this in a different color that’s it half yearly I’m hoping that by doing this question for you guys you’ll see that there is a nice technique that you can do for these questions so I’m going to take X okay so that first

X and I’m gonna go um X and then I’m going to look at the interest rate and I see that for the first four years it’s going to be compounded monthly so I’m going to go one plus uh 0.079 you can say 7.9 percent if you want and that’s compounded monthly and that’s

going to be for four years so that means I’m going to put a 48 up at the top here okay let’s scratch out the seven it’s getting in the way okay so that’s gonna be uh to the power of 48. then all that I do is I then switch over to the next interest rate remember I’m

using the formula a equals to P 1 plus I to the power of n um so I could say a equals to that over here and then my interest rate changes so um it just changes to 10.5 percent remember that what we learned in grade 11 when the interest rate changes you just add another bracket you don’t have

to you don’t have to like go recalculate everything you just add another bracket and that one’s going to be for six years so that’s going to be 6 multiplied by two which is 12. okay so there we go that is the X complete so I’ve now finished this one so I put a little tick

there for myself that one is finished now I’m going to move on to the next one which is um let me get rid of all of these things here they’re there and there so what I now do guys is I’m now going to be focusing my attention on this sixty thousand okay now that one says that

it’s got a minus so I’m going to say minus sixty thousand sorry I can’t fit everything on one line but yep it’s just the way it is um so minus sixty thousand I then look at the interest rate so remember that this T4 starts over here and I always look towards the end of my

timeline so that only has the blue one can you see that that only has the blue interest rate so I’m not going to put the red interest rate it’s only the blue one like that and that one is going to be for uh six years so six times two oops it’s not a twelve sorry sorry sorry sorry

hope no one saw that um so it’s a two at the bottom there and that’s going to be for six years so that’s going to be six times two which is 12. excellent and that one is now complete I’ve now done that one there’s nothing else that needs to be done there so I can tick

this one off then I move on to my next one which is the next 60 000 rent um and so then I’m just gonna say um let’s write this T10 over here I don’t want you guys to be confused over there T10 so now I’m going to carry on so I’m going to say uh minus another sixty

thousand rent and this one also only has the blue interest rate because um it starts over here so it’s only got three years left so I’m going to use the blue interest rate for that one as well whoopsie one plus 0.105 over 2 and that’s just going to be three years so that’s

going to be 2 times 3 which is six so now that one is complete so I can take that one off and then at the very end um this one happens right at the end so for this one I’m just gonna say um I’m just gonna say uh minus sixty thousand there is no interest for that one now here’s the

big question how much money must babawa have at the very end well think about this guys she’s busy she she put money in um for all of her children and when the last child the eight-year-old when that child reaches 18 she’s going to give that child 60 000 Rand and then what we would

assume is that babawa won’t have any money left in that account because that account was only opened in order to uh help her kids when they turn 18. she doesn’t want money left over so this final amount after she’s given away all of the 60 000 rents should be equal to zero okay

and so what I’m going to now do guys just so that I can make some more space for you guys is I am going to um actually I can write it all at the bottom here so I’m going to write this out for us once more so we can just see what it looks like properly so I’m just rewriting it now

guys in one line so it’s easier for us to um calculate and then minus 60 000 here and then all of that is equal to zero okay now guys now I’m not going to waste all of our time showing you how to calculate this now all that you are going to do is the following you are going to take all

of these values over here and you’re going to take all of that to the right hand side of the equation where the zero is okay you’re going to take all of those values to the right hand side and then once you’ve got that amount on the right hand side and you’ve added all of

that together then you’re going to divide by this part over here so that you will be able to get the X value by itself okay I’m not going to spend time on that that is easy for most of you but your final answer that you would like to reach um should be 99 699 Rand and 20 cents so that

is the amount that babalua must put into the account right now so that she can fund all of her kids at the appropriate time