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 11.4 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.)

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TomShelby TomShelby · Answer 1 · 2020-02-05T05:12:40+01:00

Answer:

A) 6,157.18

B ) 18,611.55

C) 59,501.22

Explanation:

we solve for the annuity which generates a future value of 1,000,000 in 40 years at 11.4%

[tex]FV \div \frac{(1+r)^{time} -1}{rate} = C\\[/tex]

FV 4,000,000

time 40

rate 0.114

[tex]4000000 \div \frac{(1+0.114)^{40} -1}{0.114} = C\\[/tex]

C $ 6,157.183

if time is 30 years:

[tex]FV \div \frac{(1+r)^{time} -1}{rate} = C\\[/tex]

FV 4,000,000

time 30

rate 0.114

[tex]4000000 \div \frac{(1+0.114)^{30} -1}{0.114} = C\\[/tex]

C $ 18,611.552

if time is 20 years:

[tex]FV \div \frac{(1+r)^{time} -1}{rate} = C\\[/tex]

FV 4,000,000

time 20

rate 0.114

[tex]4000000 \div \frac{(1+0.114)^{20} -1}{0.114} = C\\[/tex]

C $ 59,501.222