Suppose you wanted to have exactly 20000 in your savings

Question

Consider a savings plan with an initial deposit of $1800, an annual interest rate 3.25% compounded monthly and a monthly deposit of $120.

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

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

c. Suppose you wanted to have exactly $20000 in your savings account after 48 months at an annual interest rate of 3.25% compounded monthly and you made an initial deposit of $1800. 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.

d. 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.

1. How much is in the saving account after...

   ...1 month?	mce_markernbsp;
   ...6 months?	mce_markernbsp;
   ...1 year?	mce_markernbsp;
   ...2 years?	mce_markernbsp;

2. Repeat part (d) if the annual interest rate changes from 3.25% to 4.25%.
   How much is in the saving account after...

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