Question 7.3: Bláithín has commenced employment at a company that offers a......
Bláithín has commenced employment at a company that offers a pension in the form of an annuity that pays 5% interest per annum compounded monthly. She plans to work for 30 years and wishes to accumulate a pension fund that will pay her €2000 per month for 25 years after she retires. How much does she need to save per month to do this?
First, we determine the value that the fund must accumulate to pay her €2000 per month, and this is given by the present value of the 25-year annuity of €2000 per month. The interest rate r is 5% and as there are 12 compounding periods per year there are a total of 25 ∗ 12 = 300 compounding periods, and the interest rate per compounding period is 0.05/12 = 0.004166.
P\;\;=\;\;2000/0.004166[1-(1.004166)^{-300}]= €342, 174.
That is, her pension fund at retirement must reach €342,174 and so we need to determine the monthly payments necessary for her to achieve this. The future value is given by the formula:
F V=A{\frac{(1+i)^{n+1}-1}{i}}and so
A=F V*i{/}\left[(1+i)^{n+1}-1\right]where m = 12, n = 30 * 12 = 360 and i = 0.05/12 = 0.004166 and FV = 342174.
A = 342,174 * 0.004166/3.4863
= €408.87
That is, Bláithín needs to save €408.87 per month (€4906.44 per year) into her retirement account (sinking fund) for 30 years in order to have an annuity of €2000 per month for 25 years.