II. The Total Future Value of a Steady Stream of Payments Now, suppose we open an account and invest S100 at the beginning of every month, starting today, for 20 years. At the end of the 20 years, we make one final payment of $100 Problem 2: If we do not invest the monthly payments, how much will the account will be worth in 20 years? Remember to include the final payment! How should we go about calculating the value of the account at the end of the 20 years if we do invest? Let's first assume that the interest rate, r, is compounded monthly (so n = 12) In 20 years, the investment that we make today will be worth: r12-20 12 100 (1 + = 100( 1 + 12 In 20 years, the investment that we make in 1 month from now will be worth: 12.239 =100(1+ (Note that 19 years and 11 months is 239/12 years) In 20 years, the investment that we make in 2 months from now will be worth: T 238 100 1 =100(1+ Problem 3: What will the future value of the payment that we make 37 months from now be worth in 20 years? Express your answer in terms of r From the above, we can conclude that the amount of money we will have in 20 years will be the sum of the future values of the investments that we make every month! We will calculate this amount two different ways - by using Excel and by using finite geometric sums