Superannuation type question (1 Viewer)

[weirdguy99]

Hey!

This was from question 9 (b) of the 2005 CSSA Trial.

9 (b) On 1 July 2005, Nadia invested $12000 in a bank account that paid interest at a rate of 6% p.a., compounded annually.

(i) How much would be in the account after the payment of interest on 1 July 2015 if no additional deposits were made? (easy enough)

(ii) In fact, Nadia added $1000 to her account on 1 July each year, beginning on 1 July 2006. After the payment of interest and her deposit on 1 July 2015, how much was in her account?

For (ii), I finished up with $33670.97, as opposed to the answer's $34670.97. I went over the question again and came up with the same answer.

The answer's geometric series is (1.06^10-1)/0.06, while mine is 1.06(1.06^9-1)/0.06. This created the $1000 difference, but I don't understand where I went wrong.

Could anyone shed some light on this?

Thanks

 

[jessxxr]

maybe you forgot to include the year 2015 into it as it says she deposits money on July 1 2015 as well, so it then comes to 10 years total, lol i dnooo

 

[weirdguy99]

I'm fairly sure that I included the $1000 deposited on July 1, I actually made a note of it in my head when I was doing the question. Then I got it wrong D:

 

[OldMathsGuy]

Hey!

This was from question 9 (b) of the 2005 CSSA Trial.

9 (b) On 1 July 2005, Nadia invested $12000 in a bank account that paid interest at a rate of 6% p.a., compounded annually.

(i) How much would be in the account after the payment of interest on 1 July 2015 if no additional deposits were made? (easy enough)

(ii) In fact, Nadia added $1000 to her account on 1 July each year, beginning on 1 July 2006. After the payment of interest and her deposit on 1 July 2015, how much was in her account?

For (ii), I finished up with $33670.97, as opposed to the answer's $34670.97. I went over the question again and came up with the same answer.

The answer's geometric series is (1.06^10-1)/0.06, while mine is 1.06(1.06^9-1)/0.06. This created the $1000 difference, but I don't understand where I went wrong.

Could anyone shed some light on this?

Thanks

Ignore the initial amount and focus on the $1000 a year. She makes 10 payments but the first payment in 2006 only gets nine years worth of compound interest.

Therefore your series looks something like:

1000 x (1.06)^9 + 1000 x (1.06)^8 + ... + 1000

Reverse it around and factorise (take the 1000 out) and you get:
a = 1
r = 1.06
n = 10

Your mistake was pretty much not including the final 2015 payment of $1000 that received no interest. Hope this helps.

Best Regards
OldMathsGuy

 

[weirdguy99]

Ah, I see.

So out of four marks, how many would I have received?

 

[OldMathsGuy]

Ah, I see.

So out of four marks, how many would I have received?

Most likely 3 out of 4 as you have attacked the meat of the question correctly and only made a single error.

Best Regards
OldMathsGuy