Suppose an individual makes an initial investment of $1,000 in an account that earns 8.4%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.) (a) How much is in the account after the last deposit is made? $ _____ (b) How much was deposited? $ _____ (c) What is the amount of each withdrawal? $ _____ (d) What is the total amount withdrawn? $ _____

Let's go through this problem step by step.

### Part (a): How Much is in the Account After the Last Deposit?

To determine the account balance after the last deposit, we consider both the initial investment and the regular contributions.

The future value of the account, $ A $, after 12 years, is given by the formula:

\[
A = P(1 + r)^n + \frac{C \left((1 + r)^n - 1\right)}{r}
\]

Where:
- $ P = 1000 $ is the initial investment
- $ r = \frac{8.4\%}{12} = \frac{0.084}{12} \approx 0.007 $ is the monthly interest rate
- $ n = 12 \times 12 = 144 $ is the total number of contributions
- $ C = 100 $ is the monthly contribution

### Part (b): How Much Was Deposited?

The total amount deposited includes the initial investment plus all the monthly contributions:

\[
\text{Total Deposited} = P + C \times n
\]

### Part (c): What is the Amount of Each Withdrawal?

After 12 years, the individual starts making monthly withdrawals over the next 5 years. To find the amount of each withdrawal, we use the future value of an annuity formula, rearranged to solve for the withdrawal amount:

\[
W = \frac{A \times r}{1 - (1 + r)^{-m}}
\]

Where:
- $ A $ is the amount in the account after 12 years (from Part (a))
- $ r $ is the monthly interest rate
- $ m = 5 \times 12 = 60 $ is the number of withdrawals

### Part (d): What is the Total Amount Withdrawn?

The total amount withdrawn is simply the monthly withdrawal amount multiplied by the number of withdrawals:

\[
\text{Total Withdrawn} = W \times m
\]

Now, I'll calculate each part.It seems like I can’t do more advanced data analysis right now. Please try again later. If you still need help, I can walk you through the steps for solving this problem manually or assist with another question. Let me know how you'd like to proceed!

Explore how to calculate the future value of an investment with monthly contributions, and determine the amount of each withdrawal over a 5-year period. This problem involves compound interest and annuities, suitable for students in Grades 10-12.

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