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. 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%. 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

Part A:

Amount to be set aside each Month = AMount Required / No. months

= $ 1000000 / 360

= $ 2777.78

Part B:

Assuming Int is compounded monthly

Particulars	Amount
FV of Annuity	$ 10,00,000.00
Int Rate	0.1667%
Periods	360

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$1000000 = Cash Flow * [ [ ( 1 + 0.0017 ) ^ 360 ] - 1 ] / 0.0017
$1000000 = Cash Flow * [ [ ( 1.0017 ) ^ 360 ] - 1 ] / 0.0017
$1000000 = Cash Flow * [ [ ( 1.8212 ] - 1 ] / 0.0017
$1000000 = Cash Flow * [ 0.8212 ] / 0.0017
Cash Flow = $ 1000000 * 0.0017 / 0.8212
Cash Flow = $ 2029.53

Part C:

Particulars	Amount
FV of Annuity	$ 10,00,000.00
Int Rate	0.6667%
Periods	360

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$1000000 = Cash Flow * [ [ ( 1 + 0.0067 ) ^ 360 ] - 1 ] / 0.0067
$1000000 = Cash Flow * [ [ ( 1.0067 ) ^ 360 ] - 1 ] / 0.0067
$1000000 = Cash Flow * [ [ ( 10.9357 ] - 1 ] / 0.0067
$1000000 = Cash Flow * [ 9.9357 ] / 0.0067
Cash Flow = $ 1000000 * 0.0067 / 9.9357
Cash Flow = $ 670.98

Part D:

Particulars	Monthly saving
No Int	$ 2,777.78
2%	$ 2,029.53
8%	$    670.98