Question

Belle, who has just started her first full-time salary job is determined to have $1 million in her account by the time she retires. She is now 25 and hopes to retire at 65 years of age. Her investments have been earning 5.25% annual return and she thinks it’s realistic that can be maintained. How much would Belle have to put aside each month, in order to reach her goal? What is the total amount of money she will have saved? How much interest will have been earned?

Answer #1

Solution :-

Annual Rate of Return = 5.25%

Now Monthly Rate of Return = ( 1 + 0.0525 )^{1/12} - 1 =
1.004273 - 1 = 0.004273 = 0.4273%

Amount Required At Retirement at the age of 65 = $1,000,000

Time in Retirement = ( 65 - 25 ) = 40 Years

Total Months in 40 Years = 40 * 12 = 480

Now suppose the Amount of Monthly Deposit be X

As per data given ,

$1,000,000 = X * ( F/A , 0.4273% , 480 )

$1,000,000 = X * [ ( 1 + 0.004273 )^{480} - 1 ] /
0.004273

$4,273.128 = X * [ 7.74255 - 1 ]

X = $633.755

Therefore , Belle have to put aside each month, in order to reach her goal = $633.76

Now The Total Amount of Money she will have Saved = ( $633.755 * 480 ) = $304,202.46

Now interest that will have been earned = $1,000,000 - $304,202.46 = $695,797.54

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