Question

It is January 1st, 2021, and you are setting up a perpetuity that will allow you to withdraw R dollars at the end of April and October every year, forever. Suppose that the stated APR of the perpetuity is r > 0.

Question 1 Determine the present value of the perpetuity if
interest is compounded monthly.

Leave your answer in terms of R and r.

Question 2 Determine the present value of the perpetuity if interest is compounded continuously instead. Leave your answer in terms of R and r.

Question 3 Which of your answers (between Question 1 and
Question 2) do you expect to be larger?

This question will be hard to answer mathematically, but you should
be able to argue it using financial reasoning. In 5 sentences or
less, justify your answer.

Answer #1

It is January 1st, 2021, and you are setting up a perpetuity
that will allow you to withdraw R dollars at the end
of April and October every year, forever. Suppose that the
stated APR of the perpetuity is r > 0.
Question 1 Determine the present value of the perpetuity if
interest is compounded monthly. Leave your answer in
terms of R and r.
Question 2 Determine the present value of the perpetuity if
interest is compounded continuously instead....

Suppose that on January 1, 2018, you buy a bond for $2,000 that
will pay interest of 3.6% per year compounded continuously for 20
years. You never withdraw any of the interest earned on the
bond.
(a) What will the bond be worth on January 1, 2038?
(b) Suppose that on January 1, 2020, the prevailing rate of
interest on bonds maturing on January 1, 2038 becomes 6% per year
compounded continuously. Assume that the market value of your bond...

1, Your parents deposit $10,000 into your bank account and allow
you to withdraw $500 every month for living expenses in 2 years to
support your MBA education. What annual interest
rate does the bank pay so that you will withdraw
everything in 2 years? Please round your answer to the fourth
decimal. For example, if your answer is 1%, you should input
0.0100.
2, A preferred stock pays an annual dividend of $1.01 per share
forever. The appropriate interest...

How long will you really live for after you retire?
Unfortunately, nobody knows the answer to this question.
One approach to answering this age-old question is to consider
this: how much should you have in your retirement account upon
retiring so that you can withdraw a fixed sum forever? This may
seem odd, but it is indeed possible.
Suppose that you invest $PMT into your retirement account for 30
years at an average monthly APR of 12.5% (very possible with...

Answers currently posted for this question are incorrect. Today
you opened up a local bank account. Your plan is to make five
$4,000 contributions to this account. The first $4,000 contribution
will occur today and then every six months you will contribute
another $4,000 to the account. (So your final $4,000 contribution
will be made two years from today). The bank account pays a 6% APR
that is compounded monthly. After two years, you plan to leave the
money in...

a) on your sister’s 10th birthday, your parents want
to invest a certain amount to enable her to withdraw R25 000 every
six months from her 18th to her 24th birthday (both birthdays
included). Calculate the sum they will have to invest if compounded
interest is estimated at 12% per annum, compounded biannually.
b) What is the present value of a perpetuity that pays
R4 800 per year if the first payment does not begin until four
years later and...

QUESTION 9
Suppose you plan to retire at age 70, and you want to be able to
withdraw an amount of $83,000 per year on each birthday from age 70
to age 100 (a total of 31 withdrawals). If the account which
contains your savings earns 5.4% per year simple interest, how much
money needs to be in the account by the time you reach your 70th
birthday? (Answer to the nearest dollar.)
Hint: This can be solved as a...

You are about to buy a million dollar house with a 20 percent
down payment. The mortgage has 5 percent stated annual interest
rate, compounded monthly, and calls for equal monthly payments over
the next 30 years. The first payment is due one month from now.
What is your monthly mortgage payment?
I know the answer si 4294.57
but I am having trouble understanding the second part of the
question
The mortgage terms require that at the end of year...

1. Today you deposited $15,000 into a 5-year CD that will pay 6
percent interest. How much will you withdraw from the account in 5
years? Round to the nearest cent. Do not include any unit (If your
answer is $111.11, then type 111.11 without $ sign.)
2. You have a retirement account that earns 5 percent annual
interest with the total account balance of $400,000. How much a
year can you withdraw for next 20 years if your first...

Suppose you earned a $435,000 bonus this year and invested it at
8.25% per year. How much could you withdraw at the end of each of
the next 20 years?
Select the correct answer.
a. $45,114.15
b. $45,123.65
c. $45,133.15
d. $45,152.15
e. $45,142.6
Suppose you just won the state lottery, and you have a choice
between receiving $3,550,000 today or a 20-year annuity of
$250,000, with the first payment coming one year from today. What
rate of return is...

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