A company contributes $170 per month into a retirement fund paying 4.20% compounded monthly and employees are permitted to invest up to $ 2,800 per year into another retirement fund which pays 4.20% compounded annually.
How large can the combined retirement fund be worth in 29 years?
To calculate the combined retirement fund after 29 years, we need to calculate the future value of each contribution separately and then add them together.
First, let's start with the company contribution of $170 per month, which is made monthly at a rate of 4.20% per year compounded monthly. Let's use the formula for the future value of an ordinary annuity:
Future Value = P * [(1 + r/n)^(n*t) - 1] / (r/n)
Where:
P = Payment or contribution per period
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years
P = $170 (monthly contribution)
r = 4.20% (annual interest rate, expressed as a decimal)
n = 12 (compounding periods per year)
t = 29 (number of years)
Plugging in these values, we get:
Future Value of monthly contribution = $170 * [(1 + 0.042/12)^(12*29) - 1] / (0.042/12)
Simplifying further, we have:
Future Value of monthly contribution = $170 * [(1.0035)^(348) - 1] / (0.0035)
Calculating this expression gives us the future value of the monthly contribution.
Next, let's calculate the future value of the annual employee contribution. The employee is allowed to invest up to $2,800 per year at an interest rate of 4.20% compounded annually. Using the formula for the future value of a single amount:
Future Value = P * (1 + r)^t
Where:
P = Principal investment or contribution
r = Annual interest rate
t = Number of years
P = $2,800 (annual contribution)
r = 4.20% (annual interest rate, expressed as a decimal)
t = 29 (number of years)
Plugging in these values gives us:
Future Value of annual contribution = $2,800 * (1 + 0.042)^29
Calculating this expression gives us the future value of the annual contribution.
Finally, to calculate the combined retirement fund worth after 29 years, we simply add the future values of the monthly and annual contributions:
Combined Retirement Fund Worth = Future Value of monthly contribution + Future Value of annual contribution
Substituting the calculated future values into this formula will give you the desired result.