Question

Apply Basic Annuities:

John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $x every month into that account so that when the retires at 55, he can withdraw $2,000 every month end to support his retirement. He expects to live up till 70 years.

How much should he deposit every month into his savings account?

Answer 1

Amount required at the time of retirement=Present value of annuity=amount/periodic rate*(1-1/(1+periodic rate)^n)=2000/(6%/12)*(1-1/(1+6%/12)^(12*(70-55)))=237007.0293

Future Value of amount already saved=Future value of lumpsum=Present value*(1+periodic rate)^n=10000*(1+6%/12)^(12*(55-25))=60225.75212

Additional amount required at the time of retirement=237007.0293-60225.75212=176781.2772

Monthly deposits required=Annuity given a future value=Future value*periodic rate/((1+periodic rate)^n-1)=176781.2772*(6%/12)/((1+6%/12)^(12*(55-25))-1)=175.9866898