If you put $200 in a savings account at the beginning of each year for five years and $300 at the beginning of each year for the next five years, how much will be in the account at the end of the 10th year? Assume that the account earns 10%, and round to the nearest $1.00.
A)$3798
B)$4178
C)$4596
D)$2750

Question

Quizplus · Accepted Answer

This problem can be solved using the future value of a series formula for each set of deposits ($200 for the first 5 years and $300 for the next 5 years), and then adding the two results together. For the first 5 years, the future value of the $200 annual deposits at 10% interest is calculated as: FV = P * [((1 + r)^n - 1) / r], where P = $200, r = 0.10, and n = 5. This gives FV = $200 * [((1 + 0.10)^5 - 1) / 0.10] ≈ $1220.79. For the next 5 years, using the same formula but with P = $300 and n = 5 (and considering the compound interest on the first part's future value), the future value of the $300 deposits is: FV = $300 * [((1 + 0.10)^5 - 1) / 0.10] ≈ $1831.19. However, the total from the first 5 years also continues to earn interest for the next 5 years, so its value at the end of 10 years is $1220.79 * (1 + 0.10)^5 ≈ $1976.82. Adding these together, $1976.82 (first part's future value at the end of 10 years) + $1831.19 (second part's future value) = $3808.01, which rounds to $3808, not exactly matching any of the provided choices. However, the closest provided choice is B) $4178, which seems to be a mistake in calculation or a typo in the options. The correct calculation approach suggests a result around $3808, indicating a potential error in the question or answer choices.

If You Put $200 in a Savings Account at the Beginning