Part 1An employee contributes $ 200$200 a year (at the end of the year) to her pension plan. What would be the total contributions and value of the account after five years? Assume that the plan earns 1010% per year over the period.Part 2
A. Total contributions equal $ 800$800 and the value of the account is $ 854.70$854.70. B. Total contributions equal $ 800$800 and the value of the account is $ 976.80$976.80. C. Total contributions equal $ 1,000$1,000 and the value of the account is $ 1,098.90$1,098.90. D. Total contributions equal $ 1,000$1,000 and the value of the account is $ 1,221.00$1,221.00.

Question

Part 1An employee contributes $ 200$200 a year​ (at the end of the​ year) to her pension plan. What would be the total contributions and value of the account after five ​years? Assume that the plan earns 1010​% per year over the period.Part 2
A. Total contributions equal $ 800$800 and the value of the account is $ 854.70$854.70. B. Total contributions equal $ 800$800 and the value of the account is $ 976.80$976.80. C. Total contributions equal $ 1,000$1,000 and the value of the account is $ 1,098.90$1,098.90. D. Total contributions equal $ 1,000$1,000 and the value of the account is $ 1,221.00$1,221.00.

BlackTom AI · Accepted Answer

Question restatement: Part 1 asks for the total contributions and the value of the pension account after five years, with $200 contributed at the end of each year and an annual return of 10%. Part 2 provides four answer choices.

Option A: 'Total contributions equal $800 and the value of the account is $854.70.'
- Why this is incorrect: The total contributions over five years at $200 per year should be 5 × $200 = $1000, not $800. So the stated contributions are too low. 
- About the account value: even if we mistakenly assumed only $4 × 200 contributed, the final value would not align with the given $854.70 under a 10% return model for five years. This option therefore fails on both the contribution amount and the ending balance.

Option B: 'Total contributions equal $800 and the value of the account is $976.80.'
- Why this is incorrect: Similar to A, the total contributions are mis-stated as $800 instead of the correct $1000. The ending balance of $976.80 would require a different contribution pattern or a different interest treatment, which is not consistent with contributing $200 at year-end for five years at 10% annual growth. The mismatch in contributions makes this option invalid.

Option C: 'Total contributions equal $1000 and the value of the account is $1,098.90.'
- Why this is incorrect: The total contributions of $1000 are correct for five years at $200 each. However, the ending balance of $1,098.90 is too low for five years of 10% growth with yearly end-of-year contributions. If we compute the balance year by year with end-of-year contributions of 200 and 10% annual return, the final balance comes out around $1,221.00 (or $1,221.02 by exact calculation), not $1,098.90. This indicates an underestimation of growth or miscalculation.

Option D: 'Total contributions equal $1000 and the value of the account is $1,221.00.'
- Why this is correct: Over five years, contributing $200 at the end of each year yields total contributions of 5 × $200 = $1000. With a 10% annual return compounded annually, the balance evolves by applying 10% growth to the existing balance each year and then adding the next $200 at year-end. Calculating step by step:
  - End of year 1: 0 × 1.10 + 200 = 200.00
  - End of year 2: 200 × 1.10 + 200 = 420.00
  - End of year 3: 420 × 1.10 + 200 = 662.00
  - End of year 4: 662 × 1.10 + 200 = 928.20
  - End of year 5: 928.20 × 1.10 + 200 = 1,221.02
  This gives a final balance very close to $1,221.00 (the slight difference comes from rounding in the options). The critical pieces—the total contributions of $1000 and a final balance around $1,221—match option D.

Summary: Options A and B misstate the total contributions as $800, which is incorrect for five years of $200 deposits. Option C gives the correct total contributions but an ending balance ($1,098.90) that is inconsistent with the 10% annual growth and the given contribution schedule. Option D correctly states the total contributions as $1000 and provides an ending balance that aligns with the compound interest calculation for five end-of-year deposits of $200 at 10% per year, yielding about $1,221.00.

Homework:Chapter 13 Homework

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