Question

Derek currently has $13,976.00 in an account that pays 5.00%. He will withdraw $5,724.00 every other year beginning next year until he has taken 6.00 withdrawals. He will deposit $13976.0 every other year beginning two years from today until he has made 6.0 deposits. How much will be in the account 24.00 years from today?

Answer 1

PV in account =13976
Rate =5%
FV =PV*(1+r)^n =13976*(1+5%)^24 =45074.9968

Withdrawal next year =5724
Effective bi yearly rate =(1+5%)^2-1 =10.25%
Year after 6 withdrawals =11
FV at year 11 =PMT*((1+r)^n-1)/r)=5724*((1+10.25%)^6-1)/10.25%) =44443.7230
FV at year 24 =44443.7230*(1+5%)^13 =83805.2682

Deposit after 2 years =13976
Years after 6 deposits =12
FV at year 12 =PMT*((1+r)^n-1)/r)=13976*((1+10.25%)^6-1)/10.25% =108515.9806
FV at year 24 =108515.9806*(1+5%)^12 =194879.1103

FV at 24 years =45074.9968-83805.2682+194879.1103=156148.84