A professional plans to retire in 30 years and intends to create a personal retirement fund with
Question:
A professional plans to retire in 30 years and intends to create a personal retirement fund with quarterly contributions according to the following schedule:
• the first quarter an amount of $ X is deposited,
• the second quarter an amount of $ X * (1 + g %),
• the third quarter is deposited an amount $ X * (1 + g%) ^2,
• the fourth deposit is for $ X * (1 + g%)^3,
• the fifth deposit is for $ X * (1 + g%)^4and so on until your retirement date
• The deposit growth rate (g%) is planned equal to 1% quarterly.
The purpose of the retirement fund is to be able to initiate during your retirement period a series of semester withdrawals of magnitude $ 60,000 (equal flows) for the next 20 years after your retirement from work. Assume that withdrawals from the account start on the day of your withdrawal, and that deposits stop on the same day. Determine the size of the first deposit $ X, if your financial advisor promises you an interest rate of 9% per year compounded quarterly for the first 30 years of stay in the fund, and a rate of 12% per year compounded semi-annually for the subsequent 20 years upon retirement.
