Question

 You are graduating from college at the end of this semester and after reading the The Business of Life box in this​ chapter, you have decided to invest ​$5 , 100 at the end of each year into a Roth IRA for the next 42 years. If you earn 7 percent compounded annually on your​ investment, how much will you have when you retire in 42 ​years? How much will you have if you wait 10 years before beginning to save and only make 32 payments into your retirement​ account? How much will you have when you retire in 42 ​years?

Answer 1

First:

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                5,100.00
rate of interest per period	r=
Rate of interest per year		7.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.07*12/12	7.0000%
Number of periods
Number of years		42
Number of payments in a year		1
Total number of periods	n=	42
FV of annuity	=	5100* [ (1+0.07)^42 -1]/0.07
FV of annuity	=	1,176,224.42

Future value is 1,176,224.42

Second: 10%

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                5,100.00
rate of interest per period	r=
Rate of interest per year		7.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.07*12/12	7.0000%
Number of periods
Number of years		32
Number of payments in a year		1
Total number of periods	n=	32
FV of annuity	=	5100* [ (1+0.07)^32 -1]/0.07
FV of annuity	=	562,112.59

Answer is $562,112.59

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