Question

The objective is to accumulate $1,000,000 in savings, in 30 years from today. What amount of money must be set aside each month, to reach our goal, assuming that the money is not invested and no interest is earned? Assume that the money is placed in a checking account that pays a 2% interest rate. The interest is compounded annually. What amount must be deposited each month to reach our goal? For our third scenario, assume that the money is invested in an index fund, with an annual return rate of 8%. Because the gains are reinvested, the investment is subject to annual compounding. How does this change our calculation? Please, show your calculations and include your results in a table, for ease of comparison. Based on the above calculations, how difficult is it to become a millionaire? Please, include a discussion of each of the 3 scenarios above.

Answer 1

Scenario 1
Amount of monthly payment	future value/no . of months	1000000/(30*12)	2777.7778
You should keep 2777.78 per month to have 1000000 in your accounts after 30 years
0.166666667
Scenario 2
Amount of monthly payment =Using PMT function in MS excel	PMT(rate,nper,pv,fv,type) rate =1/12 = .16666% nper =12*30 =360 pv =0 fv=1000000 type =0	PMT(0.16666%,360,0,1000000,0)	($2,029.55)
You should keep 2029.55 per month to have 1000000 in your accounts after 30 years
Scenario 3	0.6666667
Amount of monthly payment =Using PMT function in MS excel	PMT(rate,nper,pv,fv,type) rate =8/12 = .6666% nper =12*30 =360 pv =0 fv=1000000 type =0	PMT(0.6666%,360,0,1000000,0)	($671.09)
You should keep 671.09 per month to have 1000000 in your accounts after 30 years
Scenario	Amount of monthly Payment
1	-2777.78
2	-2029.55
3	-671.09
From the comparison of the above table it can be seen that you have to invest more to become millionaire in case of scenario one beause no interest is earned on investment, it is less difficult in scenario 2 as a low rate of interest is offered and it is quite easy to become millionaire in scenario 3 as due to good rate of return and compounding of interest, it become easy to be millionaire by investing very less amount