Annuity A requires annual contributions over 5 years and pays 5% annual interest. Annuities B and C have the same interest rate and annual contributions, but have a term of 10 and 30 years respectively. Each annuity has $50,000 in it at the end of its term. Hence, the only difference between these annuity options is the payment amount and length of the plan. Which annuity has a greater amount of interest than the sum of contributions over their term?

  Annuity C

Step-by-step explanation:

The longer the term, the greater the contribution that interest makes. If we simply assume there is an answer among these choices, it will be the choice with the longest term: Annuity C.

__

For n payments, the multiplier of the payment at 5% per year is ...

  (1.05^n -1)/(0.05)

The attached graph shows this value exceeds 2n for n > 26.5. That is, for n=30, the interest earned is more than the amount contributed.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)