Question

*Round all values to 4 decimal places.

1. What is the present value of $10,000 paid at the end of each of the next 71 years if the interest rate is 8% per year?

The present value is $______*.* (Round to the nearest
cent.)

2. Assume that your parents wanted to have $110,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 5.5% per year on their investments.

**a.** How much would they have to save each year
to reach their goal?

**b.** If they think you will take five years
instead of four to graduate and decide to have $150,000 saved just
in case, how much would they have to save each year to reach their
new goal?

3. You are trying to decide how much to save for retirement. Assume you plan to save $4,500 per year with the first investment made one year from now. You think you can earn 7.5% per year on your investments and you plan to retire in 38 years, immediately after making your last $4,500 investment.

**a.** How much will you have in your retirement
account on the day you retire?

**b.** If, instead of investing $4,500 per year,
you wanted to make one lump-sum investment today for your
retirement that will result in the same retirement saving, how
much would that lump sum need to be?

**c.** If you hope to live for 29 years in
retirement, how much can you withdraw every year in retirement
(starting one year after retirement) so that you will just exhaust
your savings with the 29th withdrawal (assume your savings will
continue to earn 7.5% in retirement)?

**d.** If, instead, you decide to withdraw
$175,000 per year in retirement (again with the first withdrawal
one year after retiring), how many years will it take until you
exhaust your savings? (Use trial-and-error, a financial
calculator: solve for "N", or Excel: function NPER)

**e.** Assuming the most you can afford to save is
$900 per year, but you want to retire with $1,000,000 in your
investment account, how high of a return do you need to earn on
your investments? (Use trial-and-error, a financial calculator:
solve for the interest rate, or Excel: function RATE)

4. A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $2,000.

Each year after that, you will receive a payment on the anniversary of the last payment that is 8% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 11% per year.

**a.** What is today's value of the bequest?

**b.** What is the value of the bequest immediately
after the first payment is made?

5. You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug's profits will be $1 million in its first year and that this amount will grow at a rate of 2% per year for the next 17 years. Once the patent expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 11% per year? (Round to three decimal places.)

6. You have an investment account that started with $4,000 10 years ago and which now has grown to $12,000.

**a.** What annual rate of return have you earned
(you have made no additional contributions to the account)?

**b.** If the investment account earns 16% per year
from now on, what will the account's value be 10 years from
now?

7. You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 6% per year. What will be your annual payment if you sign this mortgage?

8. You are saving for retirement. To live comfortably, you decide you will need to save $4 million by the time you are 65. Today is your 33rd birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 6%, how much must you set aside each year to make sure that you will have $4 million in the account on your 65th birthday?

9. A local bank is running the following advertisement in the newspaper: "For just $2,000 we will pay you $140 forever!" The fine print in the ad says that for a $2,000 deposit, the bank will pay $140 every year in perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising (what is the rate of return of this investment)?

Answer #1

Question 1:

Here we have to calculate the present value of the annuity of $10,000 for 71 years at 8% interest

The present value of the annuity is calculated as PV = P*(1-(1+r)^-n)/r where

P is the annuity = 10,000

n = 71

r = 8% = 0.08

Present Value = 10,000*(1-(1+0.08)^-71)/0.08

Present value = 10,000*(1-1.08^-71)/0.08

Present Value =10,000*12.44705519

**Present Value =124,470.5519 (Rounded to four
decimals)**

**Present Value = 124,470 .55 (Rounded to the nearest
cent)**

Note: We have answered 1 full question. Only one full question with all sub-parts can be answered at a time. Kindly post the others seperately for the experts to answer

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