Pension Planning

Planning for retirement involves ensuring that enough savings are accumulated to provide a steady income after one stops working. This is typically done through regular contributions to a pension fund, which grows over time through investments and interest.

When a person retires, they begin withdrawing a fixed amount from their pension fund each year. Since the remaining funds continue to earn interest, the total amount required at retirement is often less than the total of all withdrawals. To determine how much needs to be saved before retirement, we calculate the present value of the required future withdrawals, considering the expected interest rate on the savings.

This process involves annuity calculations, where a fixed amount is withdrawn at regular intervals, and the remaining balance continues to earn interest. By using financial mathematics, we can estimate how much needs to be saved in advance to ensure financial security in retirement.

Example

infoNote

Assume Jill would like to receive a payment of €28,000 at the beginning of each year for 25 after she retires. How would money does she need to save for retirement given that the money can be invested at a rate of 3.4%.

Jill will take out her first €28000 on the day that she retires, the subsequent payments are still in her saving accounts, collecting interest, so the present value investment are usually less than €28000 and will amount to that sum once the year elapses.

\text{Pension Fund}=28000+\frac{28000}{1.034}+\frac{28000}{1.034^2}+\frac{28000}{1.034^3} +...+\frac{28000}{1.034^{24}}

=28000 \left(1+\frac{1}{1.034}+\frac{1}{1.034^2}+\frac{1}{1.034^3} +...+\frac{1}{1.034^{24}}\right)

a=1, r=\frac{1}{1.034},n=25

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

S_{25}=\frac{1(1-\left( \frac{1}{1.034}\right)^{25})}{1-\frac{1}{1.034}}=:success[€482393.60]

Pension Planning Simplified Revision Notes for Leaving Cert Mathematics

Pension Planning

Assume Jill would like to receive a payment of €28,000 at the beginning of each year for 25 after she retires. How would money does she need to save for retirement given that the money can be invested at a rate of 3.4%.

500K+ Students Use These Powerful Tools to Master Pension Planning For their Leaving Cert Exams.

Other Revision Notes related to Pension Planning you should explore