Consider a savings plan with an initial deposit of $5500, an annual interest rate 5.5% compounded monthly and a monthly deposit of $160.

Please note that in this assignment you should round the interest rate tono less than5 or 6 decimal places. Rounding to less than 5 or 6 decimal places will give incorrect answers. When entering the interest rate in any formulas within your spreadsheet you will get more accurate answers if you (for example) enter 10.25% over a period of 12 months as0.1025/12instead of0.00854.

1. State the finite difference model and its initial condition.

   (Symbolic) y₀= (Symbolic)Note: Use ONLY the variableyn. Use numbers in place of all other variables. y_{n + 1}=

2. Write the formula derived by the Algebraic Method with the numbers appropriate for this problem.

   (Symbolic)Note: Use the variablen y_n= Use the formula derived by the Algebraic Method to find the savings after four years (48 months). $

3. Suppose you wanted to have exactly $20000 in your savings account after 48 months at an annual interest rate of 5.5% compounded monthly and you made an initial deposit of $5500. What would your monthly savings have to be (how much would you have to deposit into the account each month) to achieve this goal? You may use trial-and-error in Excel or find the algebraic solution with Maple or by hand to obtain your answer. $________________________
4. Using a spreadsheet, recursively generate a table showing the amount in the savings plan over two years. Use this spreadsheet to answer the following questions.Note: Use the numbers from part (a). How much is in the saving account after...

   ...1 month?	$
   ...6 months?	$
   ...1 year?	$
   ...2 years?	$

5. Repeat part (d) if the annual interest rate changes from 5.5% to 6.5%. How much is in the saving account after...

   ...1 month?	$
   ...6 months?	$
   ...1 year?	$
   ...2 years?	$