Question

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 11.9 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 15 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 25 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a)Since he wants to become a millionaire, the current present value will be 1,000,000. You need to find monthly savings to accumulate a million at the following intervals

PVA=1 000 000

a) According to the annuity formula:

$PVA=A(\frac{(1+\frac{i}{m})^{mn}-1}{\frac{i}{m}})$

$1 000 000=A(\frac{(1+\frac{0.119}{12})^{480}-1}{\frac{0.119}{12}})$

n=40,m=12, mn=480

A=87,73

b) $1 000 000=A(\frac{(1+\frac{0.119}{12})^{300}-1}{\frac{0.119}{12}})$

40-15=25

n=25,m=12, mn=300

A=541.76

c)$1 000 000=A(\frac{(1+\frac{0.119}{12})^{180}-1}{\frac{0.119}{12}})$

40-25=15

n=15,m=12, mn=180

A=2020.75