Maths finance question (1 Viewer)

[girlworld_club]

A superannuation fund paid 6% p.a for the first 10 years and then 10% p.a after that. If thanh put $5000 into this fund at the end of each year, how much would she have at the end of 25 years.

 

[girlworld_club]

bumpity bump bump

 

[Drongoski]

If I'm not mistaken final amount = :

 

[braintic]

This is one of those poorly worded questions in this topic. The problem is the use of 'end' to mean two different things. The first 'end' refers to a time within a calendar year, ie. probably the end of December. That makes the second 'end' somewhat ambiguous. As it stands, it should be read as 'after', as in 'after 25 years', or '25 years later'.. But many people will insist (wrongly) that this 'end' means the same as the first 'end', ie. 'at the end of the 25th year', or '24 years after the first payment'. In fact, many questions will say 'at the end of the 25th year' to make it unambiguously the latter option. I have always wondered why some books (and teachers, but never HSC exams) try to confuse the issue with this wording - why would banks ask you to pay money back over 24 years, yet call it a 25 year loan (yes I know its not a home loan question)?

 

[Alexis Texas]

my question is why were you asking this at 10pm on a saturday night

...


and why is someone up at 7:30 on a Sunday perusing the mathematics forums

 

[asianese]

My question why are you posting on the thread if you don't have anything constructive to say?


I agree with braintic's discussion about the ambiguity of the question. Perhaps the questions was asking if Thanh put the money in at the beginning of each year and the interested was paid at the end of every year...this would seem to be the 'standard' type of question for such investment questions. In the light of this Drongoski's answer is valid.

 

[braintic]

and why is someone up at 7:30 on a Sunday perusing the mathematics forums

Yet apparently it is OK to be perusing the mathematics forums just 42 minutes later, is that right??
At exactly what time is the threshold of acceptability?

 

[girlworld_club]

How did you get to your answer?

 

[girlworld_club]

This is one of those poorly worded questions in this topic. The problem is the use of 'end' to mean two different things. The first 'end' refers to a time within a calendar year, ie. probably the end of December. That makes the second 'end' somewhat ambiguous. As it stands, it should be read as 'after', as in 'after 25 years', or '25 years later'.. But many people will insist (wrongly) that this 'end' means the same as the first 'end', ie. 'at the end of the 25th year', or '24 years after the first payment'. In fact, many questions will say 'at the end of the 25th year' to make it unambiguously the latter option. I have always wondered why some books (and teachers, but never HSC exams) try to confuse the issue with this wording - why would banks ask you to pay money back over 24 years, yet call it a 25 year loan (yes I know its not a home loan question)?

so how would you correctly answer this question, not taking into consideration the ambiguity of the question itself.

 

[Drongoski]

How did you get to your answer?

But can you evaluate the expression first - is the answer correct? No point explaining otherwise.

 

[girlworld_club]

what i initially was confused was by how it changes from 6% to 10%.

Since
A1 (invested in the first year) = $5000 (1.06)^24

it earns intrest for a total of 25 terms, do you calculate using 6% or 10%. You would think 6%, however after it reaches the 15th term of investment does it switch to 10%, or does it stay 6%. This is what i am more confused about. Hope i am making sense.

 

[Drongoski]

Why won't you just evaluate my expression and tell me if the answer so obtained is correct?

 

[girlworld_club]

i'm not sure i don't have the answer to the question. sorry

 

[Drongoski]

i'm not sure i don't have the answer to the question. sorry

Would have helped had you said so much earlier.

Anyway here's my reasoning:

You'd know from your lessons:

1) if you put $M at the end of each period for n periods, and interest rate per period in decimal is r, you end up with the amount:


2) if you place $M for n periods, earning interest (in decimal) at r per period compounding, you end up with the amount:

So we can treat the question in this way:

With $5000 at the end of each year for 1st 10 years, you end up with $5000[(1.06^10 - 1)/0.06] and this sum is now being left to earn 10% p.a. for the next 15 years - which applying the 2nd formula above, gives you: $5000[(1.06^10-1)/0.06] x (1 + 0.10)^15

The $5000 per year for the last 15 years, by formula 1 above, become $5000[(1.1^15 - 1)/0.1]

So at the end of 25 years you end up with the amount which is the sum of the 2 amounts.