ASAP assignment 7

Unit 7: Instructor Graded Assignment

Annuities

In this and future Instructor Graded Assignments you will be asked to use the answers you found in the Unit 1 Assignment.

Note: For these questions you need to cite a reliable source for information, which means you cannot use sites like Wikipedia, Ask.com®, and Yahoo® answers. If you do use those sites the instructor may award 0 points for your response.

The Assignment problems must have the work shown at all times. The steps for solving the problems must be explained. Failure to do so could result in your submission being given a 0. If you have any questions about how much work to show, please contact your instructor.

Assignments must be submitted as a Microsoft Word® document and uploaded to the Dropbox for Unit 7. Please type all answers directly in this Assignment below the question it applies to.

All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit.

Note: All interest rates are to be assumed to be yearly interest rates.

Question 1

(10 points)

1. You wish to deposit $500 per month into an account for 36 months. Assume your interest rate is equal to the prime interest rate.

a) How much do you have (total) in the account after 36 months?

b) How much of that total is interest?

Question 2

(10 points)

2. Two people, Ella and Jane, decide to start saving for retirement. Ella decides to invest $4000 a year into an annuity at the age of 25. At the age of 35 she stops making investments and just leaves the money there. Jane on the other hand, decides to start investing $4000 a year at the age of 40 and invests that money for every year thereafter. Assuming both retire at 70, and that the interest rate both get on their investments is 10% (compounded annually) who has the most money in their account at age 70? Explain why you pick the answer you pick.

Question 3

(10 points)

3. At the age of 30 you decide to start saving money. At first you can only afford to deposit $200 per month. However, at the age of 38 you are able to deposit $300 per month. Then at the age of 45 you raise your monthly deposit again to $500 per month. Finally at the age of 50 you get promoted to president of the company and are able to deposit $2000 per month into the account. Assuming your account is earning (prime interest rate + 4%) in interest, compounded monthly, how much do you have in your account at the age of 70? Hint: Treat each time that you change the deposit amount as a seperate annuity, and compute the future value (FV) on each annuity seperately. Assume that each annuity earns compound interest during the time it is not receiving deposits.

Essay

(15 points)

4. It is commonly assumed that the stock market yields a 10% rate or return (on average) on investments made in the market long term. Write an essay looking at the advantages and disadvantages of investing in the stock market long term.

Requirements for essay

· Write your essay in this document – do not save it in a separate file.

· You must clearly state your position with well-structured paragraphs using proper grammar, spelling, and sentence structure.

· This is not an “opinion” question – you must offer evidence to support your position, using properly-cited sources.

· Your answer must be between ¾-1 page in length.

· You must cite and reference at least one source (book, website, periodical) using APA format. The required website counts as one source

· You must state at least one clear advantage and one clear disadvantage in your essay. However more references are recommended.

· Hint: Some major stock market events to consider are the crash of 1929, the flash crash of 2011, the dot com era of the late 90's, the fast drop in value in 2007-2008 then the market's climb back up in 2009 - 2012. Research into those may help you to get started.

(I submited wrong)

(Prof send me the following)

Question 1

(10 points)

1. You wish to deposit $500 per month into an account for 36 months. Assume your interest rate is equal to the prime interest rate.

a) How much do you have (total) in the account after 36 months?

*R= 3.25%, so the interest would be .0325/12 = .0027083

*N = 36 total periods

*PMT = $500

*So we will take $500 * (1.0027083)^36-1/.0027083

*(1.0027083)^36 = 1.102264842-1 =.102264842/.0027083 = 37.75979083

*$500*37.75979083 =$18,879.90 (rounded)

b) How much of that total is interest?

*$500*36 = $18,000 Total payed in

*$18,879.90 - $18,000 = $879.90 in interest (rounded)

Question 2

(10 points)

2. Two people, Ella and Jane, decide to start saving for retirement. Ella decides to invest $4000 a year into an annuity at the age of 25. At the age of 35 she stops making investments and just leaves the money there. Jane on the other hand, decides to start investing $4000 a year at the age of 40 and invests that money for every year thereafter. Assuming both retire at 70, and that the interest rate both get on their investments is 10% (compounded annually) who has the most money in their account at age 70? Explain why you pick the answer you pick.

*First we need to calculate out Ella’s future value.

*So we determine the number of periods-age 25 to 35 is 10 years.

*So we find the corresponding table value of 10% for 10 periods, which is 15.937.

*Then we take $4,000*15.937 = $63,748 after the first ten years.

*Then we use the compound interest formula of A = P(1+r)^t

*So A = $63,748(1.10)^35 = $1,791,474.14 at the age of 70.

*Then we calculate Jane’s investment:

*10% at 30 periods = table value of 164.494

*So $4,000*164.494 = $657,976 total

*As we can see, Ella’s total amount is higher, so I would choose her method of investment.

Question 3

(10 points)

3. At the age of 30 you decide to start saving money. At first you can only afford to deposit $200 per month. However, at the age of 38 you are able to deposit $300 per month. Then at the age of 45 you raise your monthly deposit again to $500 per month. Finally at the age of 50 you get promoted to president of the company and are able to deposit $2000 per month into the account. Assuming your account is earning (prime interest rate + 4%) in interest, compounded monthly, how much do you have in your account at the age of 70? Hint: Treat each time that you change the deposit amount as a seperate annuity, and compute the future value (FV) on each annuity seperately. Assume that each annuity earns compound interest during the time it is not receiving deposits.

· First we determine the interest rate per month (this will be used in each calculation) so .0725/12 = .006041667%

· The first calculation is $200 per month for 8 years

· 8 years * 12 months = 96 periods

· so $200 [(1.006041667)^96-1/006041667]; $200[.782924464/.006041667] = $25,917.50 (rounded); then we need to take the remaining years to determine the compound interest earned on the $25,917.50; so A = P(1+r)^t, A =

$25,917.50(1.0725)^32; $243,387.55

· The second calculation is $300 per month for 7 years

· 7 years * 12 months = 84 periods

· So $300[(1.006041667)^84-1/.006041667]; $300 (.658598721/.006041667 = $32,702.83 (rounded); then we need to take the remaining years to determine the compound interest earned on $32,702.83; $32,702.83(1.0725)^25=$188,155.91

· The third calculation is $500 per month for 5 years

· 5 years * 12 months = 60 periods

· so $500[1.006041667)^72-1/.006041667]; $500(.542942381/.006041667) =$44,933.16 (rounded); then we determine the compound interest earned; $44,933.16(1.0725)^20 = $182,185.15

· The fourth calculation is $2,000 per month for 20 years

· 20 years * 12 months = 240 periods

· so $2000[(1.006041667)^240-1/.006041667], $2000(3.244556906/.006041667) = $1,074,060.16

· The final step is to add it all together, so $243,387.55 + $188,155.91 + $182,185.15 + 1,074,060.16 = $1,687,788.77 total invested by the age of 70.