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If you make an initial contribution of $8000 to a retirement account 5 years from now...

If you make an initial contribution of $8000 to a retirement account 5 years from now and make annual contributions of $8000 thereafter, after how many contributions will your balance have reached at least $1000000 if your account earns 6% annual interest?

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Answer #1

Let us understand this from the table below :

The count is the number of contributions. At the end of 36 contributions, the balance would have reached at least $1000000 at the end of year of 36th contribution i.e. beginning of the 37th year. i.e. 36 contributions are required to reach the required balance.

Contribution against count 1 is an initial amount of $ 8000. The 2nd-year contribution will be the sum of the amount accumulated at the end of 1st-year contribution + Every year contribution i.e. $ 8480 + $ 8000 = $ 16480 at the start of 2nd year. Similarly, for 3rd-year contribution will be the sum of the amount accumulated at the end of 2nd year + Every year contribution i.e. $17468.80 + $ 8000 = $ 25468.80 and so on.

Count Contribution/ Amount at the start of year Annual Interest Interest at the end of year Total Amount at the end of year Every Year Contribution
1 8000.00 6.00% 480.00 8480.00 8000
2 16480.00 6.00% 988.80 17468.80 8000
3 25468.80 6.00% 1528.13 26996.93 8000
4 34996.93 6.00% 2099.82 37096.74 8000
5 45096.74 6.00% 2705.80 47802.55 8000
6 55802.55 6.00% 3348.15 59150.70 8000
7 67150.70 6.00% 4029.04 71179.74 8000
8 79179.74 6.00% 4750.78 83930.53 8000
9 91930.53 6.00% 5515.83 97446.36 8000
10 105446.36 6.00% 6326.78 111773.14 8000
11 119773.14 6.00% 7186.39 126959.53 8000
12 134959.53 6.00% 8097.57 143057.10 8000
13 151057.10 6.00% 9063.43 160120.53 8000
14 168120.53 6.00% 10087.23 178207.76 8000
15 186207.76 6.00% 11172.47 197380.22 8000
16 205380.22 6.00% 12322.81 217703.04 8000
17 225703.04 6.00% 13542.18 239245.22 8000
18 247245.22 6.00% 14834.71 262079.93 8000
19 270079.93 6.00% 16204.80 286284.73 8000
20 294284.73 6.00% 17657.08 311941.81 8000
21 319941.81 6.00% 19196.51 339138.32 8000
22 347138.32 6.00% 20828.30 367966.62 8000
23 375966.62 6.00% 22558.00 398524.62 8000
24 406524.62 6.00% 24391.48 430916.10 8000
25 438916.10 6.00% 26334.97 465251.06 8000
26 473251.06 6.00% 28395.06 501646.13 8000
27 509646.13 6.00% 30578.77 540224.89 8000
28 548224.89 6.00% 32893.49 581118.39 8000
29 589118.39 6.00% 35347.10 624465.49 8000
30 632465.49 6.00% 37947.93 670413.42 8000
31 678413.42 6.00% 40704.81 719118.22 8000
32 727118.22 6.00% 43627.09 770745.32 8000
33 778745.32 6.00% 46724.72 825470.04 8000
34 833470.04 6.00% 50008.20 883478.24 8000
35 891478.24 6.00% 53488.69 944966.93 8000
36 952966.93 6.00% 57178.02 1010144.95 8000
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