Today is January 1. Starting today, Sam is going to contribute $140 on the first of each month to his retirement account. His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of 0.5%, how much will he have in his retirement account 35 years from now?

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Quizplus · Accepted Answer

This problem can be solved using the future value of a series formula in finance, which is used to calculate the future value of a series of cash flows at a given rate of return. Here, Sam contributes $140, and his employer contributes an additional 50% of that amount, which is $70, making the total monthly contribution $210.The formula for the future value of a series is:$$ FV = P \times \frac{(1 + r)^n - 1}{r} $$where:- $FV$ is the future value of the series,- $P$ is the payment amount per period,- $r$ is the interest rate per period,- $n$ is the total number of payments.Given:- $P = $210$ (Sam's contribution plus his employer's contribution),- $r = 0.5\% = 0.005$ (monthly interest rate),- $n = 35 \times 12 = 420$ months (since there are 35 years and 12 months in a year).Plugging these values into the formula gives:$$ FV = 210 \times \frac{(1 + 0.005)^{420} - 1}{0.005} $$$$ FV \approx $300,685.11 $$Therefore, the amount Sam will have in his retirement account 35 years from now is approximately $300,685.11.

Today Is January 1