Question

Jessica plans to retire on her 65th birthday. But she plans to work part time until she turns 70. During these years of part-time work she will neither make deposits to nor make withdrawals from her retirement account. Exactly one year after the day she turns 70 after retiring she will begin to make annual withdrawal of $117,281 from her account until she turns 89. After this final draw she wants $1.44 million remaining in her account. She will make contributions to her retirement account from her 26th birthday to her 65th birthday. In order to reach this goal what must her Contributions Be with a 6% interest rate?

Answer 1

Answer:

Annual deposit= 23,150.41

Explanation:

Giving the following information:

Exactly one year after the day he turns 70 when he fully retires, he will begin to make annual withdrawals of $117,281.00 from his retirement account until he turns 89. After this final withdrawal, he wants $1.44 million remaining in his account.

He will make contributions to his retirement account from his 26th birthday to his 65th birthday.

Assume an 6.00% interest rate.

First, we need to calculate the amount of money needed at 65.

39 years*117,281 + 1,440,000= $6,013,959

We need to calculate the value at 65:

PV= 6,013,959/(1.06^10)= $3,358,163.29

We need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (3,358,163.29*0.06)/[(1.06^39)-1]= $23,150.41