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 find out how large the combined retirement fund can be worth in 29 years, we need to calculate the individual amounts contributed by the company and employees and then calculate the compounded interest for each fund separately.

Let's start by calculating the amount contributed by the company to the retirement fund:

Given:
Monthly contribution = $170
Interest rate = 4.20% per year (compounded monthly)
Time = 29 years

To calculate how much the company contributes over 29 years, we need to multiply the monthly contribution by the number of months in 29 years:

Total company contribution = Monthly contribution * Number of months in 29 years

Number of months in 29 years = 29 * 12 = 348 months

Total company contribution = $170 * 348

Next, let's calculate the amount employees can contribute to the other retirement fund:

Given:
Annual contribution limit = $2,800
Interest rate = 4.20% per year (compounded annually)
Time = 29 years

To calculate how much the employees can contribute over 29 years, we need to multiply the annual contribution limit by the number of years:

Total employee contribution = Annual contribution limit * Number of years

Total employee contribution = $2,800 * 29

Now, let's calculate the compounded interest for each fund separately and then add them together for the combined retirement fund value.

For the company contribution:
We can use the formula for compound interest:

Future value = P * (1 + r/n)^(n*t)

Where:
P = Principal amount (Total company contribution)
r = Interest rate per period (converted to decimal form: 4.20% = 0.042)
n = Number of compounding periods per year (monthly compounding = 12)
t = Number of years

For the employee contribution:
Since the interest is compounded annually, we can use the same formula as above, but with different inputs:

Future value = P * (1 + r)^t

Where:
P = Principal amount (Total employee contribution)
r = Interest rate per period (converted to decimal form: 4.20% = 0.042)
t = Number of years

Finally, we can calculate the combined retirement fund value by adding the two future values obtained from the computations above.

Let's plug in the given values into the formulas and calculate the results step by step.