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You want to be a millionaire when you retire in 40 years. a. How much do you have to save each month if you can earn an annual return of 10.8 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How much do you have to save each month if you wait 10 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. How much do you have to save each month if you wait 20 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

Answer :

Answer: (a) $123.71

(b) $372.42

(c) $1,186.12

Explanation:

He wants to be a millionaire:

Total amount = 1,000,000

Retire in 40 years.

(a) Annual return = 10.8%

[tex]1,000,000=Monthly\ Deposit\times\frac{[(1+\frac{0.108}{12}) ^{40\times12}-1] }{\frac{0.108}{12} }[/tex]

Therefore,

Monthly deposits = $123.71

(b) If you wait for 10 years before you begin your deposits, then,

[tex]1,000,000=Monthly\ Deposit\times\frac{[(1+\frac{0.108}{12}) ^{30\times12}-1] }{\frac{0.108}{12} }[/tex]

Therefore,

Monthly deposits = $372.42

(c) If you wait 20 years before you begin your deposits, then,

[tex]1,000,000=Monthly\ Deposit\times\frac{[(1+\frac{0.108}{12}) ^{20\times12}-1] }{\frac{0.108}{12} }[/tex]

Therefore,

Monthly deposits = $1,186.12

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