Financial Maths Grade 10 | Timeline deposit and withdrawal #Finance

this question is about a person called Jane and in this question Jane is going to add more money to her bank account and also take some money out and we need to work out how much she will have at the end of five years so what a nice way to often to do these is to visualize it using a

timeline and this is something that many teachers will advise you to do so on the timeline you must simply show everything that’s happening as it’s easier to see something in a picture form instead of reading it as a whole bunch of words or sentences so Jane invests 3 000 Rand into

account so straight away Jane is going to start off by adding 3 000 Rand and I’m gonna call that t zero meaning um Time Zero because later she deposits fifteen thousand Rand so after another two years Jane will add another fifteen thousand Rand a year after that she withdraws 5 000 Rand so at

T3 she is gonna withdraw five thousand Rand withdraw means you take money out the compound interest rate is nine percent for the entire duration calculate how much Jane will have after five years so I’m gonna show you a long way and then I’m going to show you a very short way and you

can choose anyone you like but the short way is much faster and many teachers will try and encourage you to use that method but let’s start with the long way first so how long will this 3000 Rand growth imagine this is your bank account that 3 000 Rand is gonna grow for two years before you

add any more money so let’s see how much you’ll have at that point so because it’s compound interest we’ll use the compound formula and the starting amount will be three thousand Rand the interest rate is nine percent which is 0.09 and that’ll grow for two years if you

had to work all of that out you would get a value of 3564 Rand and 30 cents so that is how much Jane would have after two years she then goes to the bank and she puts in another 15 000 Rand so how much will she have on that day well she’ll take the current amount that she has which is three

five six four point Thirty and she’ll simply add fifteen thousand Rand which means that Jane now has eighteen thousand five hundred sixty four Rand and 30 cents now that amount of money there is gonna grow for how long will that still grow until the next deposit or withdrawal takes place well

that’s going to still go for another one year so let’s grow it for another one year so once again we’ll use the compound formula where the starting amount is now 18 564 Rand and 30 cents and the interest rate is 0.09 and that’s going to grow for one year and if you add or if

you calculate that you’re going to end up with twenty thousand two hundred and thirty five Rand point zero eight seven that is how much Jane has after three years at that point though at that that third year she’s gonna withdraw five thousand rounds so we have to Minus 5 000 Rand which

means that Jane only has 15 035 Rand sorry fifteen thousand 235 Rand point zero eight seven now that amount of money will still grow for how long all they’ve asked us how much will Jane have after five years so that amount of money that we have up until T3 that’s going to still grow for

another two years so once again we can use the formula and so the starting amount will be fifteen thousand two hundred sorry I keep writing a zero there 235 Grand point zero eight seven the interest rate is 0.09 and it’s going to grow for two years and so jaina will have a total of eighteen

thousand one hundred Rand and 81 cents now we’re gonna I’m gonna show you the fast way so once again let’s quickly do our timeline now when you use this trick all you do is you treat each amount on its own so this 3000 Rand how long will that be in the account for so all you do is

you look at this 3000 Rand and how many years are there from t0 to T5 well that’s five years so you do the compound formula for five years on that 3000 Rand and that’s going to give you a total of 4615 Rand and 0.871 I’m just going to use three decimal places because that’s

not our final answer then we look at this fifteen thousand Rand how long will that be in the account for well that’s going to be in the account for three years so we treat each of these amounts separately and that gives you nineteen thousand four hundred twenty five Rand point four three five

I’m just doing three decimal places and then this one is going to be well the difference between T3 and T5 is two years so we’ll do the same formula but it’ll be five thousand Rand and that’ll be for two years and that’s going to give 5940.50 now what you do is any

money that’s coming into the account you add so these two and any money that sorry not those two these two you’ll add those ones and you’ll subtract that one so it’s going to be it’s gonna be the four six one five plus the 19425.435 minus 5940.50 because the 5940 is

from the 5 000 Rand which is being taken out so you minus that one and if you do that you’re gonna get the exact same answer so just remember when you’ve got multiple deposits and withdrawals happening just treat each of them separately and then combine them at the end