Question

Derek currently has $11,916.00 in an account that pays 6.00%. He will withdraw $5,627.00 every other year beginning next year until he has taken 4.00 withdrawals. He will deposit $11916.0 every other year beginning two years from today until he has made 4.0 deposits. How much will be in the account 28.00 years from today?

Answer 1

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

=5,627/1.06+5,627/1.06^3+5,627/1.06^5+5,627/1.06^7

=17980.1264(Approx)

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

=11916/1.06^2+11916/1.06^4+11916/1.06^6+11916/1.06^8

=$35920.3413

Hence total present value=11,916-17980.1264+35920.3413

=$29856.2149(Approx)

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=29856.2149*(1.06)^28

=$152615.62(Approx)