Question

You have $51,106.03 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $250,000. You expect to earn 10% annually on the account. How many years will it take to reach your goal?

Answer 1

This can be better tabulated as below.

Year	Opening investment	Annual Deposit	Interest @ 10%	Closing Balance
1	51,106	-	5,111	56,217
2	56,217	3,000	5,922	65,138
3	65,138	3,000	6,814	74,952
4	74,952	3,000	7,795	85,747
5	85,747	3,000	8,875	97,622
6	97,622	3,000	10,062	1,10,684
7	1,10,684	3,000	11,368	1,25,053
8	1,25,053	3,000	12,805	1,40,858
9	1,40,858	3,000	14,386	1,58,244
10	1,58,244	3,000	16,124	1,77,368
11	1,77,368	3,000	18,037	1,98,405
12	1,98,405	3,000	20,140	2,21,545
13	2,21,545	3,000	22,455	2,47,000
14	2,47,000	3,000

Here we can see that we can achieve our goal at the end of year 13 or the beginning of year 14 . You can see that at the beginning of year 14 we will accumulate 2,50,000

Some important points-

1) At the beginning of year -1 we have 51,106 hence interest will accrue on this amount

2) We start depositing 3000 at the end of each year hence it is considered as an opening balance at the beginning of each year

3) When we reach the end of year 13 we will have 2,47,000 with us an additional 3000 is deposited at the end of year 13 which will fetch us 2,50,000

4 ) Interest is calaculated on the opening investment and deposit made at the end of previous year/begining of current year at a rate of 10%