Calculating the Amount Smith Need to Save for Sara
Sara is 13 years old today, she will be 17 or 18 years old by time she joins college. The concept of sinking fund will be applied to arrive at the annual contribution required (Francis, 2008).

Scenario 1: When she joins college at 17
Smith will have four years to make payments, assuming that the payments are made annually and in advance. A discounting rate of 8.5 percent will be applied and four equal payments made
Number of years = 4
Interest rate =8.5 percent
Given the future value of total payments at 36,021, the computation below is employed to arrive at the value of annual payment made (Brealey, Meyers, Allen, & Mohanty, 2008).
Future Value of Total Payments = Annual Payments (1 + 1.085 + 1.0852 +1.0853)
Future Value of total Payments/ Annual Payment = 4.5395
The computed future value of total payment is 36,021.03
Therefore periodic payments to be made by Smith for a period of 4 years is:
36,021.03/ 4.5395
= USD 7932.9968

Scenario 2:
Sara is 13 years today and is expected to join college at the age of 18 years, Smith will have five years to make payments.
Calculating the present value of future payments at an interest rate of 8.5 percent
N = 5 (using 5 years because she will be 18yr. old in 5 yrs.
Future value of period payments = Annual Payments (1+ 1.085 + 1.0851 + 1.0852+ 1.0853 +1.0854)
Future value of Periodic payments /Annual Payment = 5.925
Future value of Periodic payment 36,021.03 hence, annual payments to be made will be given by;
Annual payment = 36,021.03 / 5.925
= USD 6,079.18

Computing the Amount of Money Smith Is Required to Save on Behalf of Steve Jr.
Steve Jr. is ten years today and is expected to join school at the age of 18 years, contributions made earn an interest of 8.5 percent annually while the expected Future value of payments is USD 36,021.03.
Smith will 8 years to make contributions and contributions will be made at the beginning of every year.
Future Value of Total Payments = Annual Payments
(1 + 1.085 + 1.0852+1.0853+1.0854+1.0855+1.0856+1.0857)
Future Value of total Payments/ Annual Payment = 10.8306
The computed future value of total payment is 36,021.03
Therefore periodic payments to be made by Smith for a period of 8 years is:
=36,021.03/10.8306
Annual Payments to be made = USD 3,325.8545

Computing the Amount of Money Smith Is Require to Save on Behalf of Sam
Sam is five years today, he is expected to join college at the age of 18 years, with a future value of periodic payments at USD 36,021.0321.
Smith will make 13 equal at the beginning of every year.
Future Value of Total Payments = Annual Payments (1 + 1.085 + 1.0852+1.0853+1.0854+1.0855+1.08561.0857+1.0858+1.0859+1.08510+1.08511+1.08512)
= 22.2109
Future Value of total Payments/ Annual Payment = 22.2109
The computed future value of total payment is 36,021.03
Therefore periodic payments to be made by Smith for a period of 8 years is:
=36,021.03/22.2109
Annual Payments to be made = USD 1,621.77

Conclusion
Smith a father of three children namely Sara, Steve JR and Sam, intends to take up three policies for his children each with a future value of USD 36,021.03. His plan is to clear the payments on each saving plan before each children joins college at the age of 18 years. Upon computation a saving plan on Sara will attract an annual payment of USD 6,079, a saving plan on Steve Jr. attracts an annual payment of 3,325 while a saving plan on Sam requires an annual contribution of USD 1621.

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References
Brealey, R. A., Meyers, S. C., Allen, F., & Mohanty, P. (2008). Principles of Corporate Finance (8th ed.). New Delhi: The McGraw.Hill.
Francis, A. (2008). Business Mathematics and Statistics . Andover Hanshire: South Western Cengage Learning.
Huang, L.-F. (2018). Using App Inventor to provide the amortization schedule and the sinking fund schedule. International Journal of Financial Engineering, 1-9.
Kaplan. (2010). Financial Management ACCA Compete Text. Berkshire: Kaplan Publishers UK.
Pandey, I. M. (2006). Financial Management Ninith Edition. New Delhi: Vikas Publishing.