Answer:
Annual deposit= $3,077.99
Explanation:
Giving the following information:
Derek plans to retire on his 65th birthday.
10 years after he retires, he will neither make deposits to nor take withdrawals from his retirement account.
At his 75 birthday, he will begin to make annual withdrawals of $188,527.00 from his retirement account until he turns 92.00. He will make contributions to his retirement account from his 26th birthday to his 65th birthday.
First, we need to calculate the final value required at his 75 birthday:
Number of years= 92 - 75= 17 years
Annual withdrawl= 188,527
FV= 188,527*17= 3,204,959
Now, we need to calculate the amount needed 10 years before his retirement where he won't deposit or withdraw:
PV= FV/(1+i)^n
PV= 3,204,959/1.10^10= 1,235,650.44
Now, we can calculate the annual deposit from his 26th birthday to his 65:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
Isolating A:
A= (FV*i)/{[(1+i)^n]-1}
A= (1,235,650.44*0.10) / [(1.10^39)-1]
A= 3,077.99
