Question

A year from now, you plan to begin saving for your retirement by making a deposit into a new savings account that has an expected return of 7.5% compounded monthly. You plan to continue depositing the same amount each year until you retire in 30 years. You expect to make withdrawals in the amount of $200 from your savings account every week for 45 years after you retire. Assume you were asked to find the amount you will need to deposit into your savings account each year until you retire in order to fund your retirement. In your solution, you would need to use the annuity present value equation to find the present value at your retirement date of the withdrawals you expect to make each week during your retirement. What interest rate would you use in this equation? Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39

Answer #1

The total investment horizon is 30 years staring from today .

an total withdrawl horizon is 45 years on weekly basis.

At first we convert 7.5 % compounded montly to yearly APR .

EIR = (1+r/m)^m -1

or (1+ 0.075/12)^12 -1

or 7.763 % annualy is the rate we are going to use for calculations .

Now total number of withdrawls we have = 45 years x 52 weeks = 2340 withdrawls

Sum of withdrawl = $200

I/Y weekly rate to be used = 7.763/52 = 0.1493% on weekly basis

So the target investment corpus is

200= Px0.001493/(1- (1+0.001493)^-2340

= $129876.76 is the target investment .

Now we have to find the yearly deposits to meet the target.

FV = 129876.76

N = 30 years

Rate = 7.763 % on yearly basis

So we know

FV annuity = PMT x( (1+r)^n-1) / r)

PMT = FV / ((1+r)^n-1)/r

or

PMT = 129876.76 / ((1+0.07763)^30 -1 )/0.07763))

PMT = $1197.30 per year

A week from now, you plan to begin saving for your retirement by
depositing $200 into a new savings account that has an expected
return of 7.75% compounded monthly. You plan to continue depositing
the same amount each week until you retire in 40 years. You expect
to make withdrawals from your savings account every year for 35
years after you retire. Assume you were asked to find the amount
you will be able to withdraw each year from your...

A year from now, you plan to begin saving for your retirement by
depositing $20,000 into a new savings account that has an expected
return of 5.75% compounded monthly. You plan to continue depositing
the same amount each year until you retire in 35 years. You expect
to make withdrawals from your savings account every month for 40
years after you retire. Assume you were asked to find the amount
you will be able to withdraw each month from your...

You are 25 years old and decide to start saving for your
retirement. You plan to save $X at the end of each year (so the
first deposit will be one year from now), and will make the last
deposit when you retire at age 67. Suppose you earn 4% per year on
your retirement savings. You want the present value of your total
retirement savings to be $2Million. How do you need to save each
year (the same amount...

You are 23 years old and decide to start saving for your
retirement. You plan to save $ 6,500 at the end of each year (so
the first deposit will be one year from now), and will make the
last deposit when you retire at age 69. Suppose you earn 12% per
year on your retirement savings.
a. How much will you have saved for retirement?
b. How much will you have saved if you wait until age 40 to...

You are 30 years old and decide to start saving for your
retirement. You plan to save $ 5000 at the end of each year (so
the first deposit will be one year from now), and will make the
last deposit when you retire at age 65 Suppose you earn 11 % per
year on your retirement savings. a. How much will you have saved
for retirement?
b. How much will you have saved if you wait until age 39...

You begin saving for retirement at age 25, and you plan to
retire at age 70. You want to deposit a certain amount each month
into an account that pays an APR of 3% compounded monthly. Make a
table that shows the amount you must deposit each month in terms of
the nest egg you desire to have when you retire. (Round your
answers to the nearest cent.)

"You plan to start saving for your retirement by depositing
$9,583 exactly one year from now. Each year you intend to increase
your retirement deposit by 3%. You plan on retiring 30 years from
now, and you will receive 6% interest compounded annually. This
type of cash flow is called a geometric gradient. The formula to
calculate the present worth of a geometric gradient is found in
Table 3.6 in the textbook.
However, in year 10, you have sudden expenses,...

You are
2424
years
old and decide to start saving for your retirement. You plan to
save
$ 6 comma 500$6,500
at
the end of each year (so the first deposit will be
one year from now), and will make the last deposit
when you retire at age
6767.
Suppose
you earn
11 %11%
per
year on your retirement savings.
a.
How much will you have saved for
retirement?
b.
How much will you have saved if you wait until...

You just decided to begin saving for retirement. You will make
deposits of $1,000 per month into a retirement account that earns
8.00% p.a. The first deposit is made today and the last deposit
will be made when you retire exactly 30 years from today. The day
you retire you will buy an RV for $240,000. You will begin to make
withdrawals from the account the first month after you retire. If
you plan to live an addition 25 years,...

You just decided to begin saving for retirement. You will make
deposits of $1,000 per month into a retirement account that earns
8.00% p.a. The first deposit is made today and the last deposit
will be made when you retire exactly 30 years from today. (Note:
you make 361 total monthly deposits into your retirement account.)
You will begin to make withdrawals from the account the first month
after you retire. If you plan to live an addition 25 years...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 5 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 21 minutes ago

asked 21 minutes ago

asked 21 minutes ago

asked 40 minutes ago

asked 49 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago