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kofigc · Nov 23, 2010, 02:12 PM

Hello again everyone, I shall post my working below the question as always. Thank you all once again for your time and help - all is greatly appreciated!

Q1: A man deposits Â£1000 ever half year into a pension fund earning 6% interest per annum, compounded half yearly. Deposits are made at the start of each half year. How much will the fund be worth at the end of 7.5 years after the initial deposit?
Working Sn=a(1-r^n/1-r) so S15=1000*1.03(-0.56/-0.03) which = 1030 (18.6) = 19226.6?

ebaines · Nov 24, 2010, 07:17 AM

I get 18598.91. Why did you use 1030 for 'a' instead of 1000?

kofigc · Nov 25, 2010, 12:29 PM

Thanks for the reply :)
I tried your answer and it's still not showing as correct :S
I'm more confused than ever! :(

Unknown008 · Nov 25, 2010, 11:04 PM

Doing it manually, I get £ 25672.53...

And trying to derive the formula for this, I get:

$Money = r^n P + d(1+r + r^2 + r^3 + ... +r^{n-1})$

The second part is a geometric series with sum:

$S_n = \frac{1(1-r^n)}{1-r}$

Combining these, we get:

$Money = r^n P + d$\frac{1-r^{n-1}}{1-r}$$

Where P is the principal, d the frequent deposit, r the rate and n the number of half years.

Putting P = 1000, d = 1000, n = 15 and r = 1.06

I get £ 25672.53...