A teacher, 25, started saving for her expected retirement at 65. She planned to deposit $5,000 at the end of each year @ an annual rate of 6% compounded annually. At her retirement, she plans to withdraw a fixed amount for the first 15 years at the end of each year. And for the following 15 years, she plans to withdraw double what she withdrew in the first 15 years. If she continues to earn 6% comp. annually, what should her payments be for the first 15 years and the following 15 years?. Any help would be great. Thank you
+194 i would ask a moderator or message someone else because i cant visualize it im sorry i couldnt help
First, will have to find how much money is she able to save for 40 years at $5,000 annual deposit.
The FV of her 40 deposits @ 6% comp. annually=$773,809.83.
Second, will have to find a 2 to 1 factor to apportion her withdrawal payments for the 30 years. And that factor comes to: 17.8174133152.
Then we just divide her total savings by this last factor and we get: $773,809.83 / 17.8174133152=$43,429.98, which would her withdrawals for the first 15 years.
Finally, $43,429.98 x 2 =$86,859.96, which will be her payments for the last 15 years.
P.S. ALL THESE FORMULAE ARE USED IN THE ABOVE CALCULATIONS:
1=PV=FV[1 + R]^-N=PV OF $1 IN THE FUTURE.
2=FV=PV[1 + R]^N=FV OF $1 TODAY.
3=FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.
4=PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD.
5=PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=PMT NEEDED TO PAY OFF A LOAN OF $1
Where R=Interest rate per period, N=number of periods, P=periodic payment, PV=Present value, FV=Future value.
