Question

Derek currently has $10,109.00 in an account that pays 4.00%. He will withdraw $5,509.00 every other year beginning next year until he has taken 7.00 withdrawals. He will deposit $10109.0 every other year beginning two years from today until he has made 7.0 deposits. How much will be in the account 29.00 years from today?

Answer 1

Present value of withdrawals=Cash withdrawals*Present value of discounting factor(rate%,time period)

=5,509/1.04+5,509/1.04^3+5,509/1.04^5+5,509/1.04^7+5,509/1.04^9+5,509/1.04^11+5,509/1.04^13

=29666.6343

Present value of deposits=Cash deposits*Present value of discounting factor(rate%,time period)

=10109/1.04^2+10109/1.04^4+10109/1.04^6+10109/1.04^8+10109/1.04^10+10109/1.04^12+10109/1.04^14

=52344.4165

Hence total present value=10,109-29666.6343+52344.4165

=$32786.7822

We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period

A=32786.7822*(1.04)^29

=$102250.55(Approx)