When you retire, you wish to have $3 million in your retirement account. You decided to add $2,000 every quarter to your retirement account and invest to generate annualized return of 8% from your investment, how many years do you think it will take to have $3 million in the account

43.35 years

Explanation:

Use the following formula to determine the number of years

Future Value of Annuity = Periodic Annuity x ( 1 + Periodic Interest rate )^numbers of periods ) - 1 / Periodic Interest rate

Where

Future Value of Annuity = $3 million = $3,000,000

Periodic Annuity = $2,000 per quarter

Periodic Interest rate = Interest rate x Quarterly fraction = 8%  x 3/12 = 2%

Numbers of periods = n = ?

Placing values in the formula

$3,000,000 = $2,000 x ( 1 + 2% )^n ) - 1 / 2%

$3,000,000 / $2,000 = ( 1 + 2% )^n ) - 1 / 2%

1,500 =  ( 1.02 )^n ) - 1 / 2%

1,500 x 2% = ( 1.02 )^n ) - 1

30 = ( 1.02 )^n ) - 1

30 + 1 = 1.02^n

31 = 1.02^n

Log 31 = n log 1.02

n = Log 31 / Log1.02

n = 173.41

Now calculat ethe nUmbers of years as follow

Numbers of years = n x 3/12

Numbers of years = 173.41 x 3/12

Numbers of years = 43.35 years

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