Asked by Madison Chrisman on Jun 05, 2024

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Starting today, Stephen is going to contribute $200 on the first of each month to his retirement account. His employer will contribute an additional 50% of the amount Stephen contributes. If both Stephen and his employer continue to do this and he can earn a monthly rate of 0.75%, how much will Stephen have in his retirement account 40 years from now?

A) $936,264
B) $943,286
C) $1,404,396
D) $1,414,929
E) $1,672,413

Retirement Account

A financial account specifically designed for saving toward retirement, offering various tax advantages.

Monthly Rate

Refers to the interest or finance charge applied to a loan or credit balance on a monthly basis.

  • Comprehend and utilize the principle of time value of money in assessing financial choices.
  • Conceptualize how payment frequency and timing affect the value of annuities and loans.
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KL
Katey LaminJun 09, 2024
Final Answer :
D
Explanation :
Stephen contributes $200 each month, and his employer contributes an additional 50% of that amount, which is $100. Therefore, the total monthly contribution is $300. To find the future value of these contributions, we use the future value of an annuity formula: FV=P×((1+r)n−1r)FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)FV=P×(r(1+r)n1) , where PPP is the payment amount per period, rrr is the interest rate per period, and nnn is the total number of payments. In this case, P = $300 , r=0.0075r = 0.0075r=0.0075 (0.75% monthly interest rate), and n=40×12=480n = 40 \times 12 = 480n=40×12=480 (40 years of monthly contributions). Plugging these values into the formula gives us the future value of Stephen's retirement account. The correct answer is $1,414,929, which is option D.