Question

Derek currently has $13,772.00 in an account that pays 6.00%. He will withdraw $5,561.00 every other year beginning next year until he has taken 6.00 withdrawals. He will deposit $13772.0 every other year beginning two years from today until he has made 6.0 deposits. How much will be in the account 27.00 years from today? Answer format: Round to 2 decimal places

Answer 1

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

=5,561/1.06+5,561/1.06^2+5,561/1.06^3+5,561/1.06^4+5,561/1.06^5+5,561/1.06^6

=27345.2406

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

=13772/1.06^2+13772/1.06^3+13772/1.06^4+13772/1.06^5+13772/1.06^6+13772/1.06^7

=63888.1044

Hence total present value=13,772-27345.2406+63888.1044

=$50314.8638

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=50314.8638*(1.06)^27

=$242635.68(Approx)