Need help in Series Application; Superannuation! (1 Viewer)

[Getteral09]

Hey can anyone explain how to get the answer to this Superannuation problem:

"Liam wants to save up $15000 for a car in 5 years time. He invests $2000 at the end of each year in an account that pays 7.5% p.a. interest. How much more will Liam have to pay at the end of 5 years to make up the $15000?"

The answer to the question above is $3383.22.


Thanks.

From Getteral09

 

[jyu]

Hey can anyone explain how to get the answer to this Superannuation problem:

"Liam wants to save up $15000 for a car in 5 years time. He invests $2000 at the end of each year in an account that pays 7.5% p.a. interest. How much more will Liam have to pay at the end of 5 years to make up the $15000?"

The answer to the question above is $3383.22.


Thanks.

From Getteral09

Use A = PR^n + Q(R^n - 1)/(R - 1) to calculate the savings.
P = 0, Q = 2000, R = 1 + r/100 = 1.075, n = 5
A = 11616.78

The balance = 15000 - 11616.78 = $3383.22

:wave:

 

[Getteral09]

Where did you get the "Pr^n" from? what formula? I can't remember having to learn that in the topic of "series and sequences"...

 

[Getteral09]

Hello, there's another question on supperannuation that i can't seem to answer:

Dash and Rachel want to save up $30 000 for a desposit on a house in 6 years time. They aim to pay for half the desposit each. Dash invests an inheritance of $9000 in a bank account where it earns 8% p.a. Rachel invests $2000 at the end of each year where it earns interest of 10% p.a.

a) What is the future value of Dash's investment after 6 years?



Thanks heaps.

 

[jyu]

Where did you get the "Pr^n" from? what formula? I can't remember having to learn that in the topic of "series and sequences"...

P is the initial amount invested. In this question P = 0.

Q is amount invested at the end of each year.

Superannuation formula.

Happy 2007 :wave:

 

[jyu]

Hello, there's another question on supperannuation that i can't seem to answer:

Dash and Rachel want to save up $30 000 for a desposit on a house in 6 years time. They aim to pay for half the desposit each. Dash invests an inheritance of $9000 in a bank account where it earns 8% p.a. Rachel invests $2000 at the end of each year where it earns interest of 10% p.a.

a) What is the future value of Dash's investment after 6 years?



Thanks heaps.

Dash's investment after 6 years:

A = PR^n
= 9000(1 + 8/100)^6
=$14281.87

Happy 2006 + 1

:wave:

 

[Getteral09]

Re: Need help in Series Application; Loan Repayments

A question of loan repayments that i can't seem to figure out:

When Justin borrows $8500 at 12% p.a. over 5 years he does not have to make any repayments for the first 2 months.

a) How much does he owe after 2 months?

i know how to do the a) by using the A=PR^n to get the answer to 8670.85 but b) i can't seem to get.

b) What is the amount of each monthly repayment?

I used M= [8500((1.01)^58)(0.01)]/[(((1.01)^58) - 1)] and got 189.078. However the answer says it is 197.75.


So what other method i can use?

 

[Forbidden.]

Use A = PR^n + Q(R^n - 1)/(R - 1) to calculate the savings.
P = 0, Q = 2000, R = 1 + r/100 = 1.075, n = 5
A = 11616.78

The balance = 15000 - 11616.78 = $3383.22

:wave:

Use A = PRⁿ + Q(R^{n - 1})/(R - 1) to calculate the savings.
P = 0, Q = 2000, R = 1 + r/100 = 1.075, n = 5
A = 11616.78

The balance = 15000 - 11616.78 = $3383.22

:wave:

 

[Forbidden.]

Dash's investment after 6 years:

A = PR^n
= 9000(1 + 8/100)^6
=$14281.87

Happy 2006 + 1

:wave:

Dash's investment after 6 years:

A = PRⁿ
= 9000(1 + 8/100)⁶
=$14281.87

Happy 2006 + 1

:wave:

 

[Getteral09]

Re: Need help in Series Application; Loan Repayment

A question of loan repayments that i can't seem to figure out:

When Justin borrows $8500 at 12% p.a. over 5 years he does not have to make any repayments for the first 2 months.

a) How much does he owe after 2 months?

i know how to do the a) by using the A=PR^n to get the answer to 8670.85 but b) i can't seem to get.

b) What is the amount of each monthly repayment?

I used M= [8500((1.01)^58)(0.01)]/[(((1.01)^58) - 1)] and got 189.078. However the answer says it is 197.75.


So what other method that i can use?

 

[SoulSearcher]

Re: Need help in Series Application; Loan Repayment

Use the amount that he owes at the end of 2 months as the original amount that he needs to repay, in short:
M = [8670.85 * 1.01⁵⁸ * 0.01] / [1.01⁵⁸ - 1], then follow on from there.

 

[jyu]

Use A = PRⁿ + Q(R^{n - 1})/(R - 1) to calculate the savings.
P = 0, Q = 2000, R = 1 + r/100 = 1.075, n = 5
A = 11616.78

The balance = 15000 - 11616.78 = $3383.22

:wave:

You did not type the formula correctly!

:wave:

 

[Getteral09]

Re: Need help in Series Application; Loan repayments

Thanks guys!!

hmmmm..another question that i couldn't seem to match the answer to c):

"A store will give a loan of $5000 for furniture at 15% p.a. interest over 2 years."

a) What is the amount of each monthly instalment? which i got the answer to be 242.43.

b)If there is a special plan where there is no repayment for 3 months, find the repayment for 3 months, find the amount of each monthly instalment under this plan. i also got this answer to 282.52.

c) How much more would you pay under this special plan than with the normal loan? this question i keep getting 114.6 not 114.65. I had used (242.43 x 24)-5000= 818.40 and then do (282.52 x 21) - 5000= 932.97. From there i take 932.97 away from 818.40 to equal 114.60. But the answer says it's 114.65. How can i get to that answer?

 

[Forbidden.]

You did not type the formula correctly!

:wave:

Sorry I was attempting to place superscripts and subscripts

[sup][/sup][sub][/sub]

sup gives x²
sub gives x₂

 

[chousta]

Re: Need help in Series Application; Loan repayments

Thanks guys!!

hmmmm..another question that i couldn't seem to match the answer to c):

"A store will give a loan of $5000 for furniture at 15% p.a. interest over 2 years."

a) What is the amount of each monthly instalment? which i got the answer to be 242.43.

b)If there is a speacial plan where there is no repayment for 3 months, find the repayment for 3 months, find the amount of each monthly instalment under this plan. i also got this answer to 282.52.

c) How much more would you pay under this special plan than with the normal loan? this question i keep getting 114.6 not 114.65. I had used (242.43 x 24)-5000= 818.3977657 and then do (282.52 x 21) - 5000= 932.9740718. From there i take 932.9740718 away from 818.3977657 to equal 114.6. But the answer says it's 114.65. How can i get to that answer?

for part c ur workin seems to be correct, the reason you got a different answer is because you havnt been roundin your answers off..... usually when workin with money, or in a high school exam, you are expects to round off to 2 decimal places.

you have to think it through, before you post(sorry to say)

 

[Getteral09]

Re: Need help in Series Application; Loan repayments

I have round it off and i still got my answer to 114.60 which is wrong.

 

[toadstooltown]

Use A = PR^n + Q(R^n - 1)/(R - 1) to calculate the savings.
P = 0, Q = 2000, R = 1 + r/100 = 1.075, n = 5
A = 11616.78

The balance = 15000 - 11616.78 = $3383.22

:wave:

Do *NOT* just use a "superannuation formula" or "loan repayment" formula for questions such as these. My teacher is an HSC marker and to gain full marks in these often 2 or 3 mark questions students are required to write out payment 1, payment 2, ..., payment n (or something similar) to show / appreciate where and of what type the series is and then number crunch.

It may be boring tedious but k02033's working is how one should set out questions on applications of serious such as these.

 

[chousta]

Re: Need help in Series Application; Loan repayments

I have round it off and i still got my answer to 114.60 which is wrong.

Ok mate, post up your working and ill sift through it....generally its probably a little error in calculations, or it might just be a slight misprint. Where abouts did u get the question from??

(sorry for being lazy)

 

[Getteral09]

Re: Need help in Series Application; Loan repayments

ok. I got the question from Maths In Focus 2 in Chapter 5, Series, Ex 5.11, Q10. Do u have this book?

 

[chousta]

Re: Need help in Series Application; Loan repayments

no sorry dont have it, but considering its maths in focus it wouldn't suprise me if the answer was a misprint. If your getting the rest of the questions correct dont worry too much, also try some questions from past hsc papers, and some trials-both avail. on this site.