Julie invests $200 from her pretax pay into the investment plan and her employer matches the investment by a further 50%, so that makes $300 per month in total. This is how I interpret the question.
The growth rate I assume is 2.75% per annum. This is 2.75/12=0.2292% (11/48%) per month. Therefore, assuming that the question is asking for the annual interest compounded monthly, then after 12 monthly payments of $300 we have at the end of each month:
Month number |
Growth ($) |
1 |
300.6875 |
2 |
602.0641 |
3 |
904.1313 |
4 |
1206.8908 |
5 |
1510.3441 |
6 |
1814.4928 |
7 |
2119.3385 |
8 |
2424.8828 |
9 |
2731.1273 |
10 |
3038.0737 |
11 |
3345.7234 |
12 |
3654.0782 |
At the end of each month a further $300 is added to whatever has accumulated through interest. So, at the end of the twelfth month the total investment was $3600 which has grown to $3654.08, that is, the interest gained is $54.08. However, it depends on when interest is added. I've assumed that the initial $300 gains interest before the second payment has been made. If this is not the case, the interest after 12 months will be $45.72.
Algebraically, if m is the monthly investment and r the annual interest rate we have a geometric series:
m(1+(1+r)+(1+r)2+...+(1+r)10+(1+r)11)=m((1+r)12-1)/r. Interest=m((1+r)12-1)/r - 12m.
If m=300, this comes to $45.72. If interest is accumulated on the first payment of the year then the formula is slightly different: m(1+r)((1+r)12-1)/r - 12m.