Compound Interest Q (1 Viewer)

[Smithereens]

Tom’s father paid $500 into an account on the day Tom was born?After that, he paid $500 into the account on Tom’s bday until Tom’s 18^th bday?If the account accrued interest at 8%p.a compounded monthly, calculate how much Tom would receive on his 18^th bday.

Thanks!



Ans: $20880.97

 

[ahhliss]

Is this a superannuation question?


I was $500 off if I round it to 2 decimal places as you do with money :mad1: Here's what I did. Interest rate was 1/150 per month as a fraction. The number of payments was 19 because I counted his 18th birthday.
The first payment compounded for 12*19 time periods so 500(151/150)^228, the next 12*18 etc. Last one being 500(151/150)^12 or 500(151/150)^0=500? Is the last payment on his 17th or 18th?
The sum turned out 500(1+(151/150)^12+(151/150)^24+...+(151/150)^228)
The sum of the GP turned out (1-((151/150)^12)^19)/(1-(151/150)^12))=(1-(151/150)^228)/(1-(151/150)^12)
So my overall answer was 500(1-(151/150)^228)/(1-(151/150)^12)=$21,380.97

I know I'm wrong, but I feel close, anyone like to edit it to make it correct? Because I have an extra $500, if there was no 1 and the sequence started with (151/150)^12, the answer would work... Maybe he doesn't pay $500 on his 18th?

Also, there could be typos, typing up maths really sucks, but hopefully I have enough information for someone to get what I did and correct me.

 

[VenomP]

The reason why you are 500 dollars higher than the intended answer is because you added the 500 dollars he might have put in on the 18th birthday.

However according to the answer, he didn't.

That's the tricky part of these questions, i spose.

 

[Mark576]

The reason why you are 500 dollars higher than the intended answer is because you added the 500 dollars he might have put in on the 18th birthday.

However according to the answer, he didn't.

That's the tricky part of these questions, i spose.

It says that he deposited $500 until Tom's 18^th birthday. This means that he did not deposit any money on Tom's 18^th birthday. If he had of done so, the question would explicitly say so.

 

[ahhliss]

Ooooh ok