We want to become millionaires attaining $2 million. Our 5 th birthday is today,

Question

We want to become millionaires attaining $2 million. Our 5th birthday is today, and our grandparents give us $10,000, which we invest at 5% interest rate. Additionally, they give us $4,000 for as long as we need it to attain our goal. Our retirement will start in 65 years last for 25 years and needs $70,000 per annum. We shall pay for a 4-year degree from our pocket in 13 years at $20,000 per annum. In year 8, we take a vacation to the Greek islands, and it costs us $26,000. How old shall we be when we attain our goal?

Important Note:

This question is poorly worded by my professor. To be clear, so there is no confusion, the $4,000 that our grandparents give us to attain our goal is monthly, not yearly. Also, the $2 million is only for 2 people. And, the retirement amount is not required apart from the $2 million. I hope this helps.

I talked to my friend and this is the instructions that he gave me:

Step 1: find value of all expenses (college and vacation) in year 65.

Step 2: Present value of the retirement income in year 65.

Step 3: Total amount of pension fund in year 60 to finance these expenses and retirement

Step 4: Find the saving amount in year 65

Step 5: If she become a millionaire in year 65, we can check. But she could not become millionaire. So, it is imposible to becaome millionaire after year 65.

Within the 25 years, they're going to have a contingency of $250,000 from the $2M due to the fact they're only spending $70k/year. To spend the $2M in it's entirety, they would have to spend $70,000/year

If you calculate only the value of the deposit and annuity, they will have $2M before 65. But, because of the cost of vacation and college, they will not have $2M before 65. So, they will not have $2M at any time.

I hope these instructions help you find the solution because I am having trouble. Please, I beg you, show the full work, so I can follow it and understand it more clearly because this is for a take home test. It is very important. Thank you.

Explanation / Answer

1) VALUE OF EXPENSES IN YEAR 65

particulars amount

1.college fee in 13years 20000$ for 4years

the above amount will be paid after 13 years. it has to be brought down to present value by discounting the above expenses.

year amount discounting factor(note1) presentvalue of cash flows

1 - 4 20000 2.72 54400 (20000*2.72)

note1:- we can use annuity factor if there exists no uneven cash flows as for all the 4 years cash flow is 20000. and let interest rate for discounting to be 5%.

annuity factor =[ (1 / 1 + r) + (1 /[1+r]2) + ........]

= 1 / 1 + 0.05 + 1 / (1+0.05)2 + 1/(1+0.05)3

   =2.72   

the above value of 54400 is the present value after 13yeARS. So that value has to be brought to current value by discounting for 13years

54400 / (1.05)13 = 28850$

2.vacation to greek islands

after 8 years = 26000

it has to be discounted to present value = 26000 / (1.08)8 = 14045   

3.they going to spend 70000$ per year for 25years

year amount annuity factor presentvalue cash flows

1 - 25 70000 14.09(as done above) 986300 (value as on 65years)

so all the sum of present values 1.+2. = 28850 + 14045 = 42895

this is current value. we have to take it to 65years from now

therefore 42895 * (1.05)65    = 43895*23.84 = 1046457

so total expense as on 65 years = 1046457 + 986300(computed above)

= 2032757 = $2.032757million

2. present value of retirement income

particulars income annuity factor cashflows

grandparents given 10000 (1.05)65 = 23.83 238300

given yearly till retirement 4000(1-65yrs) 4000*(1.004)65*12 3120000 (used finance calculator)

total income = 3358300   

as 4000 receieved monthly per annum 5percent

so per month 5/12 = 0.416percent

we have to use it as r.

step 4:- total amount of saving in year 65

income in 65years - expense as on year 65

= 3358300 - 2032757

saving = 1325543$ = 1.325million $

note:- assumed 4000$ is monthly payment i think it will be appropriate and step 3 was not done due to lack of further details related to pension fund.

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