did I do this right? You are graduating from college at the end of this semester
ID: 2738938 • Letter: D
Question
did I do this right?
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 $4,400 at the end of each year into a Roth IRA for the next 44 years. If you earn 7 percent compounded annually on your investment, how mu Ch will you have when you retire in 44 years? How mu Ch will you have if you wait 10 years before beginning to save and only make 34 payments into your retirement account? How mu Ch will you have when you retire in 44 years? $ $ 3,551,467.08 How mu Ch will you have if you wait 10 years before beginning to save and only make 34 payments into your retirement account? $ $ 1,492,725.79Explanation / Answer
(a) $ 4,400 invested in Year 1 is compunded annually at 7% for 43 years, then $ 4,400 invested in Year 2 is compounded annually at 7% for 42 years, and so on and so forth
the accumulated value to be received at the end of 44 years = 4,400 (1.07)43 + 4,400 (1.07)42 + ... + 4,400 (1.07)1 + 4,400 (1.07)0
= 4,400 ((1.07)43 + (1.07)42 + ... + (1.07)1 + (1.07)0)
Here we have obtained a G.P. in which we have 44 terms, the sum of G.P. = 4,400 ((1.07)44 - 1)/ (1.07 - 1)
= $ 1,170,931.75
Thus, the investor will have $ 1,170,931.75 when he retires (and not $ 3,551,467.08)
(b) $ 4,400 invested in Year 11 is compunded annually at 7% for 33 years, then $ 4,400 invested in Year 12 is compounded annually at 7% for 32 years, and so on and so forth
the accumulated value to be received at the end of 34 years = 4,400 (1.07)33 + 4,400 (1.07)32 + ... + 4,400 (1.07)1 + 4,400 (1.07)0
= 4,400 ((1.07)33 + (1.07)32 + ... + (1.07)1 + (1.07)0)
Here we have obtained a G.P. in which we have 34 terms, the sum of G.P. = 4,400 ((1.07)34 - 1)/ (1.07 - 1)
= $ 564,338.57
Thus, the investor will have $ 564,338.57 when he retires (and not $ 1,492,725.79)
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