Question

To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $1.0 million by the end of 42 years from today. You plan to make equal annual year-end deposits into your management retirement account, which has historically yielded a 4% annual return.

1) How large must the annual deposits be in order for you to retire with your goal by the end of 42 years?

2) If you can only afford to deposit $5,000 per year in the retirement account, how much will you have accumulated for retirement at the end of 42 years?

3) If you can only afford to deposit $5,000 per year in retirement, how long will it take for your to accumulate your original retirement goal ?

Answer 1

1.Information provided:

Future value= $1,000,000

Time= 42 years

Interest rate= 4%

The amount of annual deposit to be deposited to reach the goal is calculated by entering the below in a financial calculator:

FV= 1,000,000

N= 42

I/Y= 4

Press the CPT key and PMT to compute the annual deposit.

The value obtained is 9,540.20.

Therefore, the annual deposit to be deposited to reach the goal is $9,540.20.

2.Information provided:

Annual deposit= $5,000

Time= 42 years

Interest rate= 4%

The amount accumulated at the end of 42 years is calculated by calculating by computing the future value.

Enter the below in a financial calculator to compute the future value:

PMT= 5,000

N= 42

I/Y= 4

Press the CPT key and FV to compute the future value.

The value obtained is 524,097.99.

Therefore, the amount accumulated at the end of 42 years is $524,097.99.

3.Information provided:

Future value= $1,000,000

Annual deposit= $5,000

Interest rate= 4%

The time to accumulate the orginal retirement goal is calculated by entering the below in a financial calculator:

FV= 1,000,000

PMT= 5,000

I/Y= 4

Press the CPT key and N to accumulate the orginal retirement goal.

The value obtained is 56.

Therefore, it takes 56 years to accumulate the orginal retirement goal.