Financial maths grade 11: Exam #Finance

in this question we are told that bob runs a car wash business he starts saving for new equipment by investing the first question says what effective rate will give him the same return so remember that when they say effective they are talking about the year lee interest rate because in this

one they said that it’s 7.5 per year but then they say compounded quarterly so they want to know what is the effective okay so remember that’s when you use this formula over here 1 plus e effective so let me just write that a little bit better equals to 1 plus now your teacher might

write this a little bit different they might use a different letter for example but in a nutshell this one over here is the effective and then this one here is what we call the nominal and that can be things like monthly quarterly and things like that so in this question we are trying to find the

effective so we’ll say one plus now this is the unknown then on the other side we will fall in so the nominal interest rate is seven point five percent so you might say seven point five percent i say zero 0.075 and then because it’s quarterly that means i put a 4 at the bottom and then

i put a 4 over here even though later on in the question they’re talking about 3 years and all of that you don’t say four times three over here when you’re using this formula you just make sure these two numbers are the same what i would then do is type all of this on my

calculator so long well in fact i’m not going to type it on the calculator just yet because then i have to round off and all of that stuff which i don’t want to do so i rather just leave it as it is i then take this one over to the right hand side where it will become negative one then

i can go type it all in now don’t round off guys you mustn’t round off here so what we’ll find is that the i effective is equal to zero point zero seven seven one three and then there’s that whole number then to get the percentage we just multiply that with a hundred and so

the final answer for this one will be 7.71 okay i’m not sure why um the answer that i found on the memo where i got this exam paper maybe they were doing one decimal for that question i’m not too sure but it should be 7.71 now we’re going to move on to question 2 which says that

bob deposits 10 000 rand immediately they tell us what the interest rate is and then at the end of the first year the interest rate changes again and then six made six months later the interest rate changes again and he adds more money so this is definitely something we will typically want to put

on a timeline because it just helps us to visualize everything a lot better i always like to do two timelines the one is for my payments and the other one is for my Interest Rates so we obviously start at t0 and we know that we’re going to end at t3 okay now we start off by

bob adds 10 000 rand so that’s just going to be 10 000 rand going in over there now let’s just look at the payments it says that at the end of the first year and then it says six months later okay so that means after 1.5 years so that’ll be a t 1.5 which is quite weird at 1.5

years because it was at the end of the first year they were talking over there and then they said six months later so they mean six months later than that part um he deposits 5000 rent okay so we’re going to add in 5 000 rand over there then in the timeline at the top i like to do all my

Interest Rates so we are told that the interest rate for the first year is 7.5 so up till t1 from t0 to t1 the interest rate was 7.5 percent quarterly so i’ll say 7.5 percent quarterly the interest rate then changes to 7.8 monthly but then it changes again after six months so

up to t 1.5 so that’s for six months over here the interest rate is 7.8 monthly so i’m going to say 7.8 percent and that is monthly and then it changes to 7 compounded monthly for the remainder up to t3 so then it’s going to be 7 percent monthly now the question says how much is

the investment worth at the end of the third year so the way that i do these types of questions is the following i look at the payments so there’s one and two and i only look at one of them at a time okay so the way that that works is i completely ignore this one for now and i’m gonna

take this one and i’m gonna take i’m gonna work out how much will that one be worth after three years so i’m gonna go all the way to three years some of you i know you still like to do the old and the slow grade 10 method i know that method makes more sense you know when you take

this amount and then you compound it up to there and then you add 5000 and then you compound it up to there that takes really long there are much faster ways so i’m going to completely ignore this one for now and i’m just going to take this 10 000 and i’m going to compound it all

the way to the end making sure that i also keep track of all the different Interest Rates so we know that this is all compounded and so we can say a equals p 1 plus i n that’s the formula we’re going to use okay so the total amount that this person’s going to have

so he starts with 10 000 and the first interest rate is this one over here and that’s going to be actually let me do this in a different color so the first interest rate is just going to be quarterly so that’s going to be 0.075 now you might say 7.5 percent that’s absolutely fine

if you do it like that on your calculator over four and this one’s only gonna be for one year right and so that’s gonna be a four over here because it’s one times four then i hope your teacher also explains it like this but when the interest rate changes you just open up another

bracket in fact we’re going to have that a little bit smaller so the next one is now the screen monthly one and so that’s going to be 1 plus 0.078 now when it’s monthly it’s 12. now that’s only for six months so we just put a six over there because it’s six

months then if it was six years you would say six times twelve so it’s only six months and then lastly there’s the blue interest rate now that one’s also monthly so i’ll say 0.07 over 12 and that lasts for 1.5 years and that’s so that’s going to be 18 months you

could say 1.5 times 12 if you wanted to and so there we go you could go ahead and you could work this all out you could all you could also do it all in one calculation but let’s just go break it i’m going to calculate this so long by typing this on the calculator now don’t round

off because that’s not the final answer so it’s going to be 12 4 3 4 point and then i’m just going to write all the decimals i have on my calculator there we go now we move on to the next payment and so we are done with this payment now now we move on to this one and what we do is

we take it from where it is and we drag it to the end so if you notice that the only type of interest that that one is going to experience is only going to be the seven percent it’s not going to experience the 7.8 and the 7.5 because it starts over here and then goes that way and so we can

use our normal formula so it’s going to be 5 000 now that one only experiences interest let me do it in blue it only experiences the 0.07 or you can say 7 and that’s also going to be for 18 months and if you work this one out don’t round off it’s going to be let me actually

answer down here it’s going to be five five five one point eight five nine one two and then of course we’re just gonna take these two answers and we’re just going to add them together so we can say total and then we just add i’m going to add those two numbers together

i’m not going to write it down just to save space but i’m adding them both together and that gives us seventeen nine eight six point one seven that was quite a good one thanks for watching guys