Assume you deposit $5,400 at the end of each year into an account paying 10.5 percent interest. a. How much money will you have in the account in 17 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How much will you have if you make deposits for 34 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. Future value b. Future value

Suppose you deposit m dollars the beginning of every month in a savings account that earns a monthly interest rate of r. For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest. Denote by An the amount of money in your account in the nth month. 1. Explain why A₁ = m dollars. 2. Explain why A₂ = m+m(1+r) dollars. 3. Write down explicit expressions for A3 and A4. This is the crucial step. 4. Explain why An = m+m(1 + r) + m(1 + r)² + ... +m(1 + r)"−¹ dollars. 5. Use the formula for a geometric sum to show that An = m (1 + r)” − 1 r dollars. 6. If your account has a monthly interest rate r = 0.002 and you deposit $200 monthly for 5 years, how much money will you have in your account after the 5 years? (Hint: How many months?)

You plan to deposit $5,500 at the end of each of the next 15 years into an account paying 11.3 percent interest. a. How much money will you have in the account in 15 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How much will you have if you make deposits for 30 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. Future value of 15 deposits b. Future value of 30 deposits

Use the appropriate formula located on Illustration 10-1 on page 209 to solve the problem. Bob deposits $5000 at the end of each 6 months for 14 years in an account paying 6% interest compounded semiannually A) Find the amount he will have on deposit at maturity. B) How much interest did Bob earn? Hint: Find the total amount that was deposited by multiplying the total number deposits with amount of each deposit and then subtracting this from the future value. Show the use of the appropriate formulas for each part by indicating the evaluation of the formula with information and provide the answers. Be sure to parts using the provided letters and organize your work neatly.