Jane is a very intelligent graduate of FIN 3601. As such, she knows she should will start contributing into her company's retirement plan. She decides to allocate $250 at the end of each month into her 401(k). However, her company offers a fairly generous matching program. For every dollar that Jane saves in her 401(k), her firm will add $0.50 to her account. If she is employed by this firm for 30 years and earns an average of 10.50% on her retirement savings per year, how much will Jane have in her retirement account 30 years from now? Report your answer rounded to two decimal places.

The amount that Jane will have in her retirement account 30 years from now is $943,650.37.

Explanation:

Jane’s monthly savings = $250

Amount added monthly by Jane’s firm = Jane’s monthly savings * Amount added by Jane’s firm for every dollar = $250 * $0.50 = $125

Total monthly savings to Jane’s 401(k) = Jane’s monthly savings + Amount added monthly by Jane’s firm = $250 + 125 = $375

Since Jane decides to allocate $250 at the end of each month into her 401(k), this implies the relevant formula to use to calculate the amount Jane will have in her retirement account 30 years from now is the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = M * (((1 + r)^n - 1) / r) (1)

Where,

FV = Future value or the amount that Jane will have in her retirement account 30 years from now = ?

M = Total monthly savings to Jane’s 401(k) = $375

r = Average monthly interest rate = Average annual interest rate / 12 = 10.50% / 12 = 0.1050 / 12 = 0.00875

n = number of months = number of years * number of months in a year = 30 * 12 = 360

Substituting the values into equation (1), we have:

FV = $375 * (((1 +0.00875r)^360 - 1) / 0.00875) = $375 * 2,516.40 = $943,650.37

Therefore, the amount that Jane will have in her retirement account 30 years from now is $943,650.37.

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