Final answer:
An approximate balance of an account after 30 years with monthly $100 deposits and a 2% annual interest rate can be calculated as $36,000 in principal plus compounded interest. The most reasonable estimate provided in the options, given the low-interest rate, is $54,000. The correct option is d.$54,000
Step-by-step explanation:
The student wants to know the approximate balance of an account after 30 years, with a 2% annual interest rate and monthly $100 deposits. To estimate this, one would typically use the formula for the future value of an annuity due to regular deposits and compound interest:
FV = P \times \left(\frac{\left(1 + r\right)^n - 1}{r}\right) \times \left(1 + r\right)
However, as the question seems to be asking for a rough estimate rather than a precise calculation, and as it doesn't provide options that are very close to each other, we can approximate by calculating the contributions alone and then adding some interest.
Monthly deposit over 30 years without interest: 30 years = 360 months
360 months \times $100/month = $36,000
Because we're accruing 2% interest annually, not monthly, we can expect a significant amount of interest to accumulate over the 30 years.
The interest will be compounded on both the accumulated balance and the new deposits. However, given the compounding effect, the estimate should account for much more than just $36,000.
The answer that is noticeably higher than the principal alone, yet reasonable considering the relatively modest interest rate, is most likely the correct one.
Looking at the options, we can see that option (d) $54,000 is just $18,000 above the principal which would be a reasonable amount of interest over 30 years at a 2% interest rate. The correct option is d.$54,000