Question

You are graduating from college at the end of this semester and have decided to invest ​$4,500 at the end of each year into a Roth​ IRA, which is a retirement investment account that grows tax free and is not taxed when it is​ liquidated, for the next 50 years. If you earn 10 percent compounded annually on your investment of ​$4,500 at the end of each​ year, how much will you have when you retire in 50 ​years? How much will you have if you wait 10 years before beginning to save and only make 40 payments into your retirement​ account? 

When you retire in 50 ​years, you will have ​$__________ ​(Round to the nearest​ dollar.)

Answer 1

When you retire in 50 years future value is:

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	4,500
rate of interest per period	r=
Rate of interest per year		10%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.1*12/12	10%
Number of periods
Number of years		50
Number of payments in a year		1
Total number of periods	n=	50
FV of annuity	=	4500* [ (1+0.1)^50 -1]/0.1
FV of annuity	=	52,37,588.38

when you invest only for 40 years.

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	4,500
rate of interest per period	r=
Rate of interest per year		10%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.1*12/12	10%
Number of periods
Number of years		40
Number of payments in a year		1
Total number of periods	n=	40
FV of annuity	=	4500* [ (1+0.1)^40 -1]/0.1
FV of annuity	=	19,91,666.50