Christine currently has $5000 in her 401(k) and plans to contribute $100 each month for the next 30 years into it. What will be the value of Christine's 402(k) in 30 years if the per annum rate of return is assumed to be 12% compounded monthly?
To calculate the future value of Christine's 401(k) in 30 years, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future value
PV = Present value (initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given:
PV = $5000 (present value)
r = 12% (annual interest rate = 0.12)
n = 12 (interest is compounded monthly)
t = 30 years
First, we'll calculate the monthly interest rate:
Monthly interest rate = (1 + r)^(1/n) - 1
Monthly interest rate = (1 + 0.12)^(1/12) - 1
Monthly interest rate = 0.009842
Next, we'll calculate the future value:
FV = $5000 * (1 + 0.009842)^(12*30)
FV = $5000 * (1.009842)^(360)
FV ≈ $5000 * 14.9748
FV ≈ $74,874.03
Therefore, the value of Christine's 401(k) in 30 years will be approximately $74,874.03.