Question

Dave and Sharon Sampson recently established a plan to save $300 per month (or $3,600 per year) for their children’s education. Their oldest child is six years old and will begin college in twelve years. They will invest the $300 in a savings account that they expect will earn interest of about 2% per year over the next twelve years. The Sampsons wonder how much additional money they would accumulate if they could earn 5% per year on the savings account instead of 2%. They also wonder how their savings would accumulate if they could save $400 per month (or $4,800 per year) instead of $300 per month.

1. Help the Sampsons determine how much they will have for the children’s education by calculating how much $3,600 in annual savings will accumulate to if they earn interest of (a) 2% and (b) 5%. Next, determine how much $4,800 in annual savings will accumulate to if they earn interest of (a) 2% and (b) 5%.

   Amount Saved Per Year	$3,600	$3,600
   Interest Rate	2%	5%
   Years	12	12
   Future Value of Savings

   Amount Saved Per Year	$4,800	$4,800
   Interest Rate	2%	5%
   Years	12	12
   Future Value of Savings

2. What is the impact of the higher interest rate of 5% (instead of 2%) on the Sampsons’ accumulated savings?
   

   
   
   
   

3. What is the impact of the higher savings of $4,800 (instead of $3,600) on their accumulated savings?
   

   
   
   
   

4. If the Sampsons set a goal to save $70,000 for their children’s college education in twelve years, how would you determine the yearly savings necessary to achieve this goal? How much would they have to save by the end of each year to achieve this goal, assuming a 5% annual interest rate?

   Future Value	$70,000
   Interest Rate	5%
   Years	12
   Savings Needed Each Year

Answer 1

Amount Saved Per Year	3600	3600	Impact
Interest Rate	0.02	0.05
Years	12	12
Future Value of Savings	$48,283.52	$57,301.66	$9,018.13
Amount Saved Per Year	4800	4800
Interest Rate	2%	5%
Years	12	12
Future Value of Savings	$64,378.03	$76,402.21	$12,024.18

Future Value	$70,000
Interest Rate	5%
Years	12
Savings Needed Each Year	$4,397.78

Workings

Book1 - Excel AutoSave ff Sign in E Share O Tell me what you want to do View File Review Help Home Insert Draw Page Layout Formulas Data Insert A^ A Calibri General 10 Delete Conditional Format as Cell Sort & Find & Paste $ - % 9 58 8 BIU Format - Filter - Select - Formatting - Table - Styles Clipboard Styles Alignment Number Cells Editing Font fx Amount Saved Per Year A14 3600 14 Amount Saved Per Year 15 Interest Rate 16 Years 3600 Impact 0.02 0.05 12 12 17 Future Value of Savings =C17-B17 =FV(B15,B16,-B14) =FV(C15,C16,-C14) 18 4800 19 Amount Saved Per Year 4800 20 Interest Rate 0.02 0.05 21 Years 12 12 22 Future Value of Savings =FV(B20,B21,-B19) =FV(C20,C21,-C19) =C22-B22 23 24 25 Future Value 26 Interest Rate 27 Years 70000 0.05 12 Savings Needed Each Year 28 =PMT(B26,B27,-B25) 29 30 ш