Help pleaseee (1 Viewer)

[vivswithluv]

A superannuation fund paid 6% pa for the first 10 yrs and then 10% pa after that. If Thanh put $5000 into the fund at the beginning of each year, how much would she have at the end of 25yrs??
Financial questions are the worst

 

[Nav123]

I mean there is a formula you know lol.. but it depends on how frequently it is compounded though, if it is monthly it is: A = $ 40,517.22

When we say pa (per annum) it is compounded yearly.

So:







and so on for 10 years:



Using the GP sum formula:



Now using AND 5000 for the next year, then 5000 for the subsequent years:





and so on for 15 years:



again using the GP sum formula;



evaluating that should give you the answer.

 

[BenHowe]

This questions is poorly worded but these sorts of problems you encounter in actuarial studies.

The reason that it's a poor question is because of the uncertainty of a 27th payment i.e. is the end of the 25th year immediately before the payment then due at the beginning of the 26th or immediately after?

Nav123, draw a timeline, it’ll help

 

[vivswithluv]

When we say pa (per annum) it is compounded yearly.

So:







and so on for 10 years:



Using the GP sum formula:



Now using A_10 for the next year, then 5000 for the subsequent years:





and so on for 15 years:



again using the GP sum formula;



evaluating that should give you the answer.

The question came from Maths In Focus and the textbook's answer was $466 563.74. I followed your working out it came out to be $445 677.50

 

[Nav123]

The question came from Maths In Focus and the textbook's answer was $466 563.74. I followed your working out it came out to be $445 677.50

Hey, I fixed it up, for there is a payment of 5000 which I missed, which gives your answer.

 

[Roy G Biv]

I am perplexed do you use the compound interest formula in this kind of a question, or is there another formula. At a glance I thought it was just a compound interest question..

This is an extension of compound interest.

In a compound interest question, you start off with ONE sum of money, which gets compounded over time.

In this question, we are putting multiple sums of money (at the start of every year actually), and EACH OF THOSE SUMS gets compounded separately. We use our knowledge of geometric series to add up all these separately compounding sums to get a total sum.

Someone has put up a solution on top - you can have a look and see if you understand. If you're not sure, you need to (re)learn the topic 'applications of series and sequences to finance'. It may appear in your textbook as 'superannuation and investments' or something like that.