Question

in some european countries such as germany. a person will retire after 40 years if working. Assume that you decide to live and work in germany and plan to retire in this country. How much should you set aside per year (annual payment). starting from the end of first working year, if you are planning to have €1,000,000 immediately after retirement. consider a discount rate of 6.8% per year.

Answer 1

The amount to be set aside per year (annual payment) is calculated by using the Future Value Ordinary Annuity Formula

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

Future Value = €1,000,000

Annual Interest Rate (r) = 6.80% per year

Number of years until retirement (n) = 40 Years

Annual Payment (P) = ?

Therefore, Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

€1,000,000 = P x [{(1 + 0.068)⁴⁰ - 1} / 0.068]

€1,000,000 = P x [(13.89472 – 1) / 0.068]

€1,000,000 = P x [12.89472 / 0.068]

€1,000,000 = P x 189.628380

P = €1,000,000 / 189.628380

P = €5,273.47

“Therefore, he has to set aside €5,273.47 per year to accumulate €1,000,000 after 40 years on his retirement”