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you are graduating from college at the end of this semester and have decide to i

ID: 2631196 • Letter: Y

Question

you are graduating from college at the end of this semester and have decide to invest 4000 dollars 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 40 years. if you earn 9 percent compounded annually on your investment of 4000 at the end of each year, 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? please do step by step. thank you

Explanation / Answer

Net worth after 40 years of the 4000 paid in year 1 = 4000 x (1.09)^39

Net worth after 40 years of the 4000 paid in year 2 = 4000 x (1.09)^38

......

Net worth after 40 years of the 4000 paid in year 40 = 4000 x (1.09)^0

Total = 4000 x (1.09)^0 + 4000 x (1.09)^1 + 4000 x (1.09)^2 + ........... + 4000 x (1.09)^38 + 4000 x (1.09)^39

=> Total = 4000 x ((1.09)^40 - 1) / (1.09 - 1) = 1351529.78

If you make only 30 payments.

Total = 4000 x (1.09)^0 + 4000 x (1.09)^1 + 4000 x (1.09)^2 + ........... + 4000 x (1.09)^28 + 4000 x (1.09)^29

=> 4000 x ((1.09)^30 - 1) / (1.09 - 1) = 545230.15