Question

Scenario

Larry and Beth are both married, working adults. They both plan for retirement and consider the $6,000 annual contribution a must.

First, consider Beth's savings. She began working at age 20 and began making an annual contribution to her IRA of $6,000 each year until age 32 (12 contributions). She then left full-time work to have children and be a stay-at-home mom. She left her IRA invested and plans to begin drawing from her IRA when she is 65.

Larry started contributing to his IRA at age 32. In the first 12 years of his working career, he used his discretionary income to buy a home, upgrade the family cars, take vacations, and pursue his golfing hobby. At age 32, he made his first $6,000 contribution to an IRA and contributed $6,000 every year up until age 65 (33 contributions). He plans to retire at age 65 and make withdrawals from his IRA.

Both IRA accounts grow at an 8% annual rate. Do not consider any tax or inflation effect.

Instructions: Please show work and answer in the below Chart/format only

Investor	Up to Age 32	Age 32 up to 65	Total FV
Beth
Larry

Answer 1

Beth Started Saving at age of 20  began making an annual contribution to her IRA of $6,000 each year until age 32 (12 contributions).

So at the age of 32 His value of Investment will be

FV32 =  

Here PMT = Annual contribution 6000

i = Interest Rate = 8% = 0.08

n = No of Contribution = 12

Now FV32 =

= 18.977 * 6000

=113862.7588

Now the value of this FV32 when age will become 65 will be

FV65 = FV32 * ( 1 + i ) ^ n  

Here n = 65 - 32 = 33 Years

i = Interest Rate = 8% = 0.08

FV65 = 113862.7588 * 1.08 ^ 33 = 14,43,329.982 ~ 14,43,330

Now Considering Larrys Saving

He did not save anything till the age of 32

After that He started saving of Annual 6000 for the next 65 - 32 = 33 Years

So at the age of 65 His value of Investment will be

FV65 =

Here PMT = Annual contribution 6000

i = Interest Rate = 8% = 0.08

n = No of Contribution = 33

= 145.9506 * 6000

= 875703.7226 ~ 875704

So answer As per Table :