Answer:
The ira will contain $228,278.05 when he retires at age 65. This is 6.04 times the amount of money he deposited.
Step-by-step explanation:
In order to solve this problem, we can make use of the following formula:
[tex]FV=PMT[\frac{(1+i)^{n}-1}{i}][/tex]
Where:
FV= Future value of the ira
PMT= the amount of money you deposit each month
i= is the interest rate per period
n=number of periods
in this case we will assume the interest will be compounded each month.
So:
FV this is what we need to know.
PMT= $75 the amount he will deposit each month
t = 42 years,
this is 65-23=42
n=42 years * 12 months/year = 504 months
i=0.07/12
So we can now use the given formula:
[tex]FV=PMT[\frac{(1+i)^{n}-1}{i}][/tex]
[tex]FV=75[\frac{(1+\frac{0.07}{12})^{504}-1}{\frac{0.07}{12}}][/tex]
So we get:
FV=$228,278.05
which is the amount of money he will have after 42 years.
In total, he deposited:
$75*504months = $37,800
so he will have:
[tex]\frac{228,278.05}{37,800}=6.04[/tex] times the amount of money he deposited throughout this time.
