1. ## Tricky Superannuation Problem

You are 44 years old, you wish to retire at 65.

You earn $75,000 a year and already have$100,000 in your super account.

You have an average annual super rate of 5.1%.

Calculate by formula the future value of your superannuation if your contributions continue to be 9% of your income but your income increases on average by 3% per annum.

The only formula given is,

Sn = a[(1+r)^n -1] ÷ r

Where a = repayment, (monthly, fortnightly etc)
r = growth rate, eg
nominal interest rate per annum ÷ number of interest periods per year

and n =
time in years * number of interest periods per year

dont even know if thats the right formula to be using, i think a new formula needs to be developed im not sure

thanks for the help anyway guys

2. Originally Posted by I Drink and Derive
You are 44 years old, you wish to retire at 65.
You earn $75,000 a year and already have$100,000 in your super account.
You have an average annual super rate of 5.1%.
Calculate by formula the future value of your superannuation if your contributions continue to be 9% of your income but your income increases on average by 3% per annum.
The only formula given is,
Sn = a[(1+r)^n -1] ÷ r
75000 * .09 = 6750 ; these are contributions without the 3% increase

That formula gives you the future value of annual deposits:
FV = 6750[(1 + .051)^(65-44) - 1] / .051

You also need the future value of the 100,000; 100000(1 + .051)^21

Are you able to follow that? What is the result of each?

3. try this out

$\displaystyle 100,000\left( {1.051} \right)^{21} + 75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21} - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}$

4. Jonah, in this portion: 75,000(0.09)(1.03)
I don't think the 1.03 is required.
But works fine otherwise.

5. Originally Posted by Wilmer
Jonah, in this portion: 75,000(0.09)(1.03)
I don't think the 1.03 is required.
But works fine otherwise.
typing is torture due to keyboard error
3 possibilities

possibility 1: 1st contrribution is included in $100,000$\displaystyle
\left\{ {\left[ {100,000 - 75,000\left( {0.09} \right)} \right] + 75,000\left( {0.09} \right)} \right\}\left( {1.051} \right)^{21} +
\displaystyle
75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21} - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}
\displaystyle
\Leftrightarrow 100,000\left( {1.051} \right)^{21} + 75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21} - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}
$possibility 2: 1st contrribution is not included in$100,000

$\displaystyle \left[ {100,000 + 75,000\left( {0.09} \right)} \right]\left( {1.051} \right)^{21} + 75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21} - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}$

possibility 3: 1st contribution is on 45th birthday

$\displaystyle 100,000\left( {1.051} \right)^{21} + 75,000\left( {0.09} \right)\frac{{\left( {1.051} \right)^{21} - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}$

6. Roger!