Question

Derek currently has $10,108.00 in an account that pays 6.00%. He will withdraw $5,123.00 every other year beginning next year until he has taken 5.00 withdrawals. He will deposit $10108.0 every other year beginning two years from today until he has made 5.0 deposits. How much will be in the account 25.00 years from today?

Answer 1

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

=5,123/1.06+5,123/1.06^3+5,123/1.06^5+5,123/1.06^7+5,123/1.06^9

=19401.9755

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

=10,108/1.06^2+10108/1.06^4+10108/1.06^6+10108/1.06^8+10108/1.06^10

=36114.4466

Hence total present value=10,108-19401.9755+36114.4466

=$26820.4711

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=26820.4711*(1.06)^25

=$115110(Approx)