Answer:
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.
