Joseph asks…

## Can anyone give me a clue how to work these problems?

*P4-4 For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the **rate** specified over the given period.

Case Signgle Cash Flow Interest **Rate** Deposit Period

A $200.00 5% 20

B 4,500 8 7

C 10,000 9 10

D 25,000 10 12

E 37,000 11 5

F 40,000 12 9

*P4-9 Present value calculation

Without referring to tables or to the preprogrammed function on your financial calculator, use the basic formula for present value, along with the given opportunity cost, i, and the number of periods, n, to calculate the present value interest factor in each of the cases shown in the accompanying table. Compare the calculated value to the table value.

Case Opportunity cost, i Number of periods, n

A 2% 4

B 10% 2

C 5% 3

D 13% 2

*P4-25 Value of a mixed stream-For each of the mixed streams of cash flows shown in the following table, determine the future value at the end of the final year if deposits are made at the beginning of each year into an account paying annual interest of 12%, assuming that no withdrawals are made during the period.

Cash flow stream

Year A B C

1 $ 900 $30,000 $1,200

2 1,000 25,000 1,200

3 1,200 20,000 1,000

4 10,000 1,900

5 5,000

*P4-31 Relationship between future value and present value—Mixed stream

Using only the information in the accompanying table, answer the questions that follow.

Year (t) Cash flow Future value interest factor at 5% (FVIF5%,n)

1 $ 800 1.050

2 900 1.102

3 1,000 1.158

4 1,500 1.216

5 2,000 1.276

A) Determine the present value of the mixed stream of cash flows using a 5% discount **rate**.

B) How much would you be willing to pay for an opportunity to buy this stream, assuming that you can at **best** earn 5% on your investments?

C) What effect, if any, would a 7% rather than a 5% opportunity cost have on your analysis? (Explain verbally.)

*P4-37 Annuities and compounding- Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest **rate** of 8%.

A) Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn, if

a. $300 is deposited annually and the credit union pays interest annually.

b. $150 is deposited semiannually and the credit union pays interest semiannually.

c. $75 is deposited quarterly and the credit union pays interest quarterly.

B) Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an **annuity**.

*P4-43 Loan amortization schedule

Joan Messineo borrowed $15,000 at a 14% annual **rate** of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments.

A) Calculate the annual, end-of-year loan payment.

B) Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

C) Explain why the interest portion of each payment declines with the passage of time.

*P4-51 Interest **rate** for an **annuity**

Anna Waldheim was seriously injured in an industrial accident. She sued the responsible parties and was awarded a judgment of $2,000,000. Today, she and her attorney are attending a settlement conference with the defendants. The defendants have made an initial offer of $156,000 per year for 25 years. Anna plans to counteroffer at $255,000 per year for 25 years. Both the offer and the counteroffer have a present value of $2,000,000, the amount of the judgment. Both assume payments at the end of each year.

A) What interest **rate** assumption have the defendants used in their offer (rounded to the nearest whole percent)?

B) What interest **rate** assumption have Anna and her lawyer used in their counteroffer (rounded to the nearest whole percent)?

C) Anna is willing to settle for an **annuity** that carries an interest **rate** assumption of 9%. What annual payment would be accept

### Pension Forecast answers:

You’ll have to do your own homework.

Richard asks…

## help with Micro Economic problem on lottery annuity?

If any one can help me, it would be greatt

You win a small lottery and have the choice of 2 ways to be paid. you can accept the money in a lumpsum (payout scheme X) or in a series of payment over time (payout scheme Y) if you pick X, you get $2740 today. If you pick Y, you get 3 payments of $1000 today, 1000 one year from today, and 1000 two years from now.

At an interest **rate** of 9% per year, the winner would be better off accepting ______ (X or Y) since it has the greater present value

At an interest **rate** of 11%per year, the winner would be better off accepting _______(x or y) since it has the greater present value

Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence she has just won another lottery with the same payout schemes. She must make a quick decision about wether to collect her money under X or Y. What is the **best** advice to give your friend?

A. payout scheme X is always better

B. Payout scheme Y is always better

C. It will depend on the interest **rate**; advise her to get a calculator

D. none of these answers is good advice

### Pension Forecast answers:

This is not too difficult. You simply need to calculate the Present Value of the stream of payments under each condition. In the first case, this would be:

$1,000+$1,000/(1.09)^1+$1,000/(1.09)^2 = $2,759.11

Similarly, if you had an interest rate of 11%, the calculation would be this:

$1,000+$1,000/(1.11)^1+$1,000/(1.11)^2 = $2,712.53.

The general formula is for an annuity amount of (p) over time period (t) for a given interest rate (i) over a number of time periods (n) the Present Value should be:

PV=p+p/(1+i)^t1+p/(1+i)^t2+p/(1+i)^t3…

Where the number of payments depends on the number of time periods over which the annuity will pay out.

This equation says that the total value of the annuity will increase for every additional year the annuity pays out, but each succeeding payout will be smaller in present value terms because it is further away in time. You can keep extending this equation out for any number of periods

So the answers to your questions are under a 9% interest rate, you would be happier with the annuity, since the Present Value of the stream of payments would be higher than what you are offered as a lump sum.

With an 11% interest rate, you would be happier with the lump sum, since the Present Value of the stream of payments would be lower than what you are offered as a lump sum.

As for your lucky friend, the answer would depend on what interest rate she could get. She would have to do the math to figure it out.

Either way, you would not be losing a lot of money by choosing incorrectly (less than $30 in the worst case) so it doesn’t really matter much. But don’t say that on your homework, the teacher might not take it well.

Lizzie asks…

## In the bank, how should I allocate my money?

A bank rep was encouraging me not to keep all my money in saving & checking & CDs but to put it also in bonds, and other plans. They said that stocks is not as stable as bonds. They have so many other long-term plans, **annuity**, etc; where they claim have a higher **rate**. I don’t want to lose all my money. I am conservative. Which is the **BEST** area(s) to put my money?

### Pension Forecast answers:

Conservative in this day and age is just begging the government to steal your money through taxes and inflation. “Please Uncle Sam, take all my money. Here it is for you to plunder.”

First of all your bank is correct, stocks are not as stable as bonds. That is a given. But stocks unlike bonds and CDs over the long term do have the tendency to keep you ahead of inflation. Currently they do not.

You are asking this question at a very opportune time. Stocks are down about 20% more or less. Some more, some less. Do you like to go shopping for sales? Well stocks are currently on sale.

Keep some of your money in CDs and in your savings account by all means. Maybe as much as 15% of your assets or perhaps even as much as 50% after a prolonged bull market. But right now, think stocks.

There is risk. No doubt about it. You could easily loose 20% by investing in stocks during the short term, but over a 10 year period you should expect about a 10% annual return especially at today’s prices. Sure beats 0.2% of a savings account and 3.5% of a 1 year CD.

Forget buying investments through your bank. There are much better ways that will yield you much better yields. Banks will stear you towards investments that pay them high returns, not you.

An investment that has a promise of being relatively safe, and I do mean relative, is PRWCX T Rowe Price Capital Apprecial Fund. Minimum investment is $2500. The year average annual return is 9.9%, not too bad. It wil probably beat anything your bank has to offer hopefully. But the future is uncertain and it may not. Keep that in mind.

Http://www.troweprice.com/common/indexFundFacts/0,0,ticker=PRWCX,00.html?src=Mflanding&scn=select_a_no_load_mutual_fund&ddown=Select_Fund_by_Name&origins=prospect

There are other opportunities out there. That is just one that has in the past prooved somewhat conservative in nature. Check it out.

Ken asks…

## Interest Rates / Annuities /Etc. What is the formula for this problem?

Bob makes his first deposit into an IRA earning % compounded annually on the day he turns 22 and his last deposit on the day he turns 44. (23 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn % interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires?

Just looking for the formula(s) that i’ll need for this problem

i can solve them no need to waste anymore of your time

**best** answer goes to the first to give me the correct formulas

i appreciate it alot

thank u thank u

Bob makes his first $950 deposit into an IRA earning 7.5% compounded annually on the day he turns 22 and his last $950 deposit on the day he turns 44. (23 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn 7.5% interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires?

could u actually try solving it because i got a “wrong answer”

HOORAY

got it

thank u very much, **best** answer to you sir!

### Pension Forecast answers:

There is NOT enough information to solve this problem. You should gives us how much money that he deposit in each year and the interest rate that he earns in order to calculate the future value of the IRA using the formula FVn = (PMT*{[(1+i)^(n1)]-1/i})*[(1+i)^(n2)] where FVn is the future value of the annuity at his 65th birthday, PMT is the annual deposit that he deposited until he turns 44, n= total number of years which he invest=44, n1=the number of years which he makes deposits= 23, n2=the number of years that he still earns interest=65-44=21, i= the annual interest rate.

EDITED.

FV = (950*{([(1+7.5%)^(23)]-1)/7.5%})

*[(1+7.5%)^(21)]

FV =247394

The IRA worths $247394 when Bob retires.

Betty asks…

## help. Annuities homework!!?

1.Mike’s Sport Shop deposits $3,600 at the end of each year for 12 years at 7% annual interest.

a. How much will this ordinary **annuity** be worth at the end of the 12 years? (5 points)

Answer: $30,240

b.How much more will this **annuity** be worth (**annuity** due) if Mike deposits the money at the beginning of each year instead of at the end of each year? (5 points)

Answer: It would be the same

2.Barb and John Reed want to know how much they must deposit in a retirement savings account today to have payments of $1,750 every six months for 15 years. The retirement account is paying 8% annual interest, compounded semiannually. (5 points)

Answer:

3.Lena Dimock is saving for her college expenses. She sets aside $200 at the beginning of each three months in an account paying 8% annual interest, compounded quarterly. How much will Lena have accumulated in the account at the end of four years? (5 points)

Answer:

Part II. Case Study

Julie has just completed the rigorous process of becoming a Certified Financial Planner (CFP). She is looking forward to working with individuals on saving for retirement. She would like to show her clients the value of an **annuity** program as one of the **best** options for investing current earnings in a tax-deferred account.

1.If a client puts the equivalent of $55 per month, or $660 per year, into an ordinary **annuity**, how much money would accumulate in 20 years at 3% compounded annually? (5 points)

Answer:

2.Jackie, a 25 year old client, want to retire by age 65 with $2,000,000. How much would she have to invest annually, assuming a 6% **rate** of return? (5 points)

Answer:

3.Another client, Wynona, decides that she will invest $5,000 per year in a 6% **annuity** for the first ten years, then $6,000 for the next ten years, and then $4,000 per year for the last ten years, how much will she accumulate? [Hint: Treat each ten-year period as as separate **annuity** and compute the Future Value. After the ten years, assume that the value will continue to grow at compound interest for the remaining years of the 30 years. Use tables from Unit 6 to compute compound interest.] (5 points)

### Pension Forecast answers:

Your first two answers are so far off, that I don’t think I can help you.

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