You plan to open a retirement account. Your employer will match 50 percent of your deposits up to a limit on the match of $2500 per year.

You believe the fund will earn 12 percent per year over the next 30 years, and you will make 30 deposits of $5000, plus 50 percent employer matching, totaling $7500 per year.

A) How much money will be in the account immediately after the last deposit?

B) How much total money will you put into the fund?

C) How much total money will your employer put into the fund?

D) How much will be the total investment earnings?

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No problem! I'll be glad to help you with these calculations. Let's break it down step by step:

A) To calculate the amount of money that will be in the account immediately after the last deposit, we need to calculate the future value of each deposit including the employer matching, and then sum them up.

To calculate the future value of each deposit, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Number of Periods

In this case, the present value is $7,500 (your deposit plus the employer matching), the interest rate is 12% (0.12), and the number of periods is 30 (for 30 years of deposits). Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + 0.12)^30

Calculating this, the future value of each deposit is approximately $1,189,214.45. Since there are 30 deposits, we multiply this value by 30 to get the total amount immediately after the last deposit:

Total after last deposit = $1,189,214.45 * 30

Therefore, the amount in the account immediately after the last deposit is approximately $35,676,433.50.

B) To calculate the total amount of money you will put into the fund, we need to multiply the annual deposit amount ($7,500) by the number of years (30):

Total money you will put into the fund = $7,500 * 30

This gives us a total of $225,000.

C) Your employer matches 50% of your deposits up to a maximum limit of $2,500 per year. Since your deposits are $5,000 per year, the employer will contribute $2,500 per year. To calculate the total contribution from your employer, we multiply this annual amount by the number of years (30):

Total money your employer will put into the fund = $2,500 * 30

This gives us a total of $75,000.

D) To calculate the total investment earnings, we subtract the total amount you put into the fund (from part B) from the total amount in the account immediately after the last deposit (from part A):

Total investment earnings = Total after last deposit - Total money you put into the fund

Total investment earnings = $35,676,433.50 - $225,000

Therefore, the total investment earnings amount to approximately $35,451,433.50.

So, to summarize:

A) The amount in the account immediately after the last deposit is approximately $35,676,433.50.
B) The total amount you will put into the fund is $225,000.
C) The total amount your employer will put into the fund is $75,000.
D) The total investment earnings amount to approximately $35,451,433.50.

I hope this helps! Let me know if you have any other questions.