We already have been given all the information we need to solve for this- it's just really extensive, so bare with me here.
With our initial deposit of $150 in January, we give 10% of the current value in the following month. This means 10% of 150 will be deposited into the checking account in February, and so on for the rest. I will work this out.
10% of 150 = 15; we deposit $15 into the account in February. 10% of 165 = 16.5; we deposit $16.5 into the account in March. 10% of 181.5 = 18.15; we deposit $18.15 into the account in April. 10% of 199.65 = 19.965; we deposit $19.96 in May (as we don't have an economical value worth a thousandth of a dollar in this problem). 10% of 219.61 = 21.961; we deposit $21.96 in June. 10% of 241.57 = 24.157; we deposit $24.15 in July. 10% of 265.72 = 26.572; we deposit $26.57 in August.
Our total value is $292.29, although if we added the thousandths, we'd have $292.31; therefore your answer is going to be D.) $292.31