(Future value of an ordinary annuity)You are graduating from college at the end
ID: 2797734 • Letter: #
Question
(Future value of an ordinary annuity)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 $4,700 at the end of each year into a Roth IRA for the next 40 years. If you earn 9 percent compounded annually on your investment, how much will you have when you retire in 40 years? How much will you have if you wait 10 years before beginning to save and only make 30 payments into your retirement account?
How much will you have when you retire in 40 years?
$__(Round to the nearest cent.)
Explanation / Answer
1st case FV = $1588047.49
2nd case FV = $640645.43
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Annuity is series of equal cash flows for certain period of time, if periodic cash flow is P, number of period is n, and interest per period is r then future value of cash flow will be
FV of annuity = P [(1 + r)^n - 1]/ r
Let's put the values in the formula,
= 4700[(1 + 0.09)^40 - 1]/ 0.09
= 4700[(1.09 )^40 - 1]/ 0.09
= 4700 ( 31.4094200539893 ) - 1/ 0.09
= 4700 ( 30.4094200539893 )/ 0.09
= 4700 * 337.882445044326
= 1588047.49170833
So FV of 4700 received for 40 period is 1588047.49
If the deposits is made after 10 years
Let's put the values in the formula,
= 4700[(1 + 0.09)^30 - 1]/ 0.09
= 4700[(1.09 )^30 - 1]/ 0.09
= 4700 ( 13.2676784691313 ) - 1/ 0.09
= 4700 ( 12.2676784691313 )/ 0.09
= 4700 * 136.307538545903
= 640645.431165744
So FV of 4700 received for 30 period is 640645.43
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Hope this answer your query.
Feel free to comment if you need further assistance. J
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