financial (1 Viewer)

stressedadfff

Well-Known Member
Joined
May 8, 2021
Messages
1,404
Gender
Female
HSC
2021
guys i suck at finance idk what to do i just don t understand it we covered it in the last two weeks of last term and its so difficult to understand what the teachers saying from online udihhufkhdsh
can someone please explain the following pls
Screen Shot 2021-09-27 at 12.49.02 pm.pngScreen Shot 2021-09-27 at 12.49.19 pm.png
 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,644
Gender
Male
HSC
N/A
Ok, the idea here is that an amount of money, $P (the PRINCIPAL) is invested. It earns interest at 4.8% per annum, compounded quarterly (so paid each quarter), and dividing by 4, we get an interest rate of 1.2% per quarter. A withdrawal is made after the interest is paid each quarter, and this problem has called this $R... an unusual choice as R usually relates to rate, with monthly payments as M and quarterly payments as M or Q. Nonetheless, it is R in this problem.

Let $An be the amount of money in the account after n quarters.

So, $A0 is the amount after zero quarters... that is, as Maxim walksaway from the teller having made the deposit of $P. That is:


One quarter later, the amount is


After the second quarter, the amount is


And so on, for every quarter, giving the general formula:


which is given in the question.

These recurrence relations are great for calculations in Excel, as shown in the question. Column B gives the initial deposit, A0 = P = 750,000, which is the opening value for finding A1. Column C calculates the interest added over the quarter, while column D subtracts the withdrawal $R = 17,800, and the amount at the end of the quarter is the starting balance plus interest minus withdrawal.

So, we have cell E2 = B2 + C2 - D2 and thus value "B" is 750,000 + 9,000 - 17,800 = $741,200.

This value then becomes the opening balance for the next quarter. Interest (value "A") is 1.2% x $741,200 = $8,894.40.
So, A2 = 741,200 + 8,894.40 - 17,800 = $732,294.40.

This is an easy process for a computer to calculate, working out each quarter's interest and adding it to the end-of-the-previous-quarter total, then subtracting the withdrawal, to get the new end-of-quarter total, and doing this over and over and over to find when the account runs out of money. It's a shit way to calculate for a human, though, as it involves tedious and repetitive calculations with plenty of opportunities for mistakes.

So, parts (a) and (b) are testing whether you understand the quarter-by-quarter process, while part (c) is testing whether you understand how to use sequences and series to side step the repetitive approach.

The trick to part (c) is to do the derivation above but with the inclusion of the previous values. That is:


We can now find the solution we seek, when the account is empty, by setting An = 0 and finding n:


This is a nasty-looking equation, so to make it easier, let's give our goal a name... Let , and so we have:


So, after 59 quarters = 14 years and 9 months, the amount Maxim has remaining is


but it is worth noting that, from his initial $750,000, Maxim will have withdrawn $17,800 x 59 = $1,050,200.
 

stressedadfff

Well-Known Member
Joined
May 8, 2021
Messages
1,404
Gender
Female
HSC
2021
Ok, the idea here is that an amount of money, $P (the PRINCIPAL) is invested. It earns interest at 4.8% per annum, compounded quarterly (so paid each quarter), and dividing by 4, we get an interest rate of 1.2% per quarter. A withdrawal is made after the interest is paid each quarter, and this problem has called this $R... an unusual choice as R usually relates to rate, with monthly payments as M and quarterly payments as M or Q. Nonetheless, it is R in this problem.

Let $An be the amount of money in the account after n quarters.

So, $A0 is the amount after zero quarters... that is, as Maxim walksaway from the teller having made the deposit of $P. That is:


One quarter later, the amount is


After the second quarter, the amount is


And so on, for every quarter, giving the general formula:


which is given in the question.

These recurrence relations are great for calculations in Excel, as shown in the question. Column B gives the initial deposit, A0 = P = 750,000, which is the opening value for finding A1. Column C calculates the interest added over the quarter, while column D subtracts the withdrawal $R = 17,800, and the amount at the end of the quarter is the starting balance plus interest minus withdrawal.

So, we have cell E2 = B2 + C2 - D2 and thus value "B" is 750,000 + 9,000 - 17,800 = $741,200.

This value then becomes the opening balance for the next quarter. Interest (value "A") is 1.2% x $741,200 = $8,894.40.
So, A2 = 741,200 + 8,894.40 - 17,800 = $732,294.40.

This is an easy process for a computer to calculate, working out each quarter's interest and adding it to the end-of-the-previous-quarter total, then subtracting the withdrawal, to get the new end-of-quarter total, and doing this over and over and over to find when the account runs out of money. It's a shit way to calculate for a human, though, as it involves tedious and repetitive calculations with plenty of opportunities for mistakes.

So, parts (a) and (b) are testing whether you understand the quarter-by-quarter process, while part (c) is testing whether you understand how to use sequences and series to side step the repetitive approach.

The trick to part (c) is to do the derivation above but with the inclusion of the previous values. That is:


We can now find the solution we seek, when the account is empty, by setting An = 0 and finding n:


This is a nasty-looking equation, so to make it easier, let's give our goal a name... Let , and so we have:


So, after 59 quarters = 14 years and 9 months, the amount Maxim has remaining is


but it is worth noting that, from his initial $750,000, Maxim will have withdrawn $17,800 x 59 = $1,050,200.
thank you so much I got none of that I'm so bad omg, could you please explain why to get A you times by 1.2%
 

CM_Tutor

Moderator
Moderator
Joined
Mar 11, 2004
Messages
2,644
Gender
Male
HSC
N/A
* because A is interest earned, and it is at a rate of 1.2%

* I'm sad to hear that none of that made sense to you, can you point to what is confusing you? Maybe someone else can explain it better / more clearly than I have. :(
 

stressedadfff

Well-Known Member
Joined
May 8, 2021
Messages
1,404
Gender
Female
HSC
2021
Ok, the idea here is that an amount of money, $P (the PRINCIPAL) is invested. It earns interest at 4.8% per annum, compounded quarterly (so paid each quarter), and dividing by 4, we get an interest rate of 1.2% per quarter. A withdrawal is made after the interest is paid each quarter, and this problem has called this $R... an unusual choice as R usually relates to rate, with monthly payments as M and quarterly payments as M or Q. Nonetheless, it is R in this problem.

Let $An be the amount of money in the account after n quarters.

So, $A0 is the amount after zero quarters... that is, as Maxim walksaway from the teller having made the deposit of $P. That is:


One quarter later, the amount is


After the second quarter, the amount is


And so on, for every quarter, giving the general formula:


which is given in the question.

These recurrence relations are great for calculations in Excel, as shown in the question. Column B gives the initial deposit, A0 = P = 750,000, which is the opening value for finding A1. Column C calculates the interest added over the quarter, while column D subtracts the withdrawal $R = 17,800, and the amount at the end of the quarter is the starting balance plus interest minus withdrawal.

So, we have cell E2 = B2 + C2 - D2 and thus value "B" is 750,000 + 9,000 - 17,800 = $741,200.

This value then becomes the opening balance for the next quarter. Interest (value "A") is 1.2% x $741,200 = $8,894.40.
So, A2 = 741,200 + 8,894.40 - 17,800 = $732,294.40.

This is an easy process for a computer to calculate, working out each quarter's interest and adding it to the end-of-the-previous-quarter total, then subtracting the withdrawal, to get the new end-of-quarter total, and doing this over and over and over to find when the account runs out of money. It's a shit way to calculate for a human, though, as it involves tedious and repetitive calculations with plenty of opportunities for mistakes.

So, parts (a) and (b) are testing whether you understand the quarter-by-quarter process, while part (c) is testing whether you understand how to use sequences and series to side step the repetitive approach.

The trick to part (c) is to do the derivation above but with the inclusion of the previous values. That is:


We can now find the solution we seek, when the account is empty, by setting An = 0 and finding n:


This is a nasty-looking equation, so to make it easier, let's give our goal a name... Let , and so we have:


So, after 59 quarters = 14 years and 9 months, the amount Maxim has remaining is


but it is worth noting that, from his initial $750,000, Maxim will have withdrawn $17,800 x 59 = $1,050,200.
fo you know whether they would be this hard for the hsc
 

stressedadfff

Well-Known Member
Joined
May 8, 2021
Messages
1,404
Gender
Female
HSC
2021
* because A is interest earned, and it is at a rate of 1.2%

* I'm sad to hear that none of that made sense to you, can you point to what is confusing you? Maybe someone else can explain it better / more clearly than I have. :(
oh NOOOOO AS IN it makes sense but i didnt get any of them correct when i did it sorry for the confusion!
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top