Question

Questions 8 & 9

Verizon LTE 9:23 PM Back AECN 452 Ho... ue: Thursday, January 24, 2019 l. (3 points) Suppose you have $1,500 you'd like to invest. If you can earn 9% compounded annually for the next three years, how mach will you have at that time? 2 4 points) How does your answer change if compounding occurs more frequently, monthly? How about daily compounding? say 3. (3 points) Using the Rule of 72, how long before your $1,500 doubles to $3.000 (assume 9% 4. (4 points) On the day you leave for college, suppose your grandmother pulls you aside and tells you that if you graduate on time in four years, she'll give you $20,000 Assuming a discount rate is 8%, she offers you an amount today that is just as good (assuming annual compounding for four years). How much does she offer you? 5. (4 points) After thinking about it a little more, your Grandmother points out that graduating on time is 46 months from the time you leave for college if you leave in August and graduate in May four years later. In addition, there is no guarantee that you l graduate on time or graduate at all for that matter. Therefore, she adds 4% to the discount rate for the uncertainty. Assuming monthly compounding (46 months), at a 12% discount rate, how much does she ofler you? 6. (12 polnts) In 1626, Peter Minuit is said to have purchased Manhattan Island from the Lenape Indians for beads and trinkets worth S24. Assuming an 8.5% annual rate of return on the $24 and 392 years total, what would the $24 be worth today assuming annual compounding? What about monthly compounding? Daily? Continously? 7. (6 points) When you retire, you'd like to have S3m saved up. Assuming you start with $1,000 and can earn 8.5% compounded monthly, how much do you need to save each month to accomplish your goal if you plan to work for 48 years? 8. (6 points) What is the monthly impact of starting your retirement planning with $1,000? 9. (10 points) At the end of the 48 years of work, you'll be 70 years old and assume you have accomplished your goal of having $3m saved. You plan to travel extensively and estimate that you'll require $240,000 per year to cover all of your living and travel expenses. If yo can keep your money safely invested and earning a 3% annual rate of return, how old will you be when you must die so as not to be a drag on the living? Dashboard Calendar To Do Notifications Inbox

Answer 1

Question 9:

Total savings = $3,000,000

Yearly Requirement = $240,000

Rate of return on investment = 3%

Annuity Payment:

P = (r*PV)/ [1 - {1/ (1+r)ⁿ}]

Where P = Payment; r = rate per period; PV = Present Value; n = number of periods

In the present case P = $240,000; r = 3%; PV = $3,000,000; n = yet to find

By substituting values in the formula,

$240,000 = (3% * $3,000,000)/ [1 - {1/ (1+3%)ⁿ}]

$240,000 = $90,000/ [1 - {1/ (1+3%)ⁿ}]

1 - {1/ (1+3%)ⁿ} = $90,000/ $240,000

1 - {1/ (1+3%)ⁿ} = 0.375

1 - 0.375 = 1/ (1+3%)ⁿ  

0.625 = 1/ (1+3%)ⁿ  

(1+3%)ⁿ = 1/ 0.625

(1+0.03)ⁿ = 1.6

(1.03)ⁿ = 1.6

Now you can find the value of n by trial and error method. That means you substitute numbers in the numerical order then you arrive at 16, which satisfies the equation.

Now the person is at 70 years of age. So after spending 16 years of time then there will be no money with him if he spends $240,000 from his savings of $3,000,000. So the age at that point would be 86 years (70+16).

Question 8:

The question was about the monthly impact of starting retirement planning with $1,000. According to me there will be a lot of impact if I start my retirement planning with $1,000 because the amount of money that I am keeping aside for the retirement plan is minimal. Which means I still have so much of money to spend on a day to day basis. And which turns me to explore new places, try different new things, etc. I can also travel around the world while earning instead of at retirement. Because I love travelling it makes me more energetic to work and live happily. And at the time of retirement I can have my small amount of fund which helps me to live for a quite number of years happily.