Answer:
The answer $6,964.4726324 per year
Explanation: The following elements are to be considered in this case:
- The total amount required for Linda's education is $132,000 ($33,000*4)
-Parents had already started investing $5,300 per year for the past five years. This is a stream of even cash flows, at an interest rate. Considering we are at the point before our parents decided to invest the $5,300 and we want to determine the future value of this fixed payments, we will consider the formula below:
Future Value FV = Cash flow per period C * ([1 + i]^n - 1 )/i where i is the interest rate and n the number of times or periods
FV= $5,300 * ([1 + 0.11]^5 - 1 )/0.11
FV= $5,300 * 6.22780141
FV= $33,007.347473
Considering they will continue to save $5,300 for five more years, we can adjust the above formula and obtain the future value of the fixed payment of $5,300 over a period of 10 years
FV= $5,300 * ([1 + 0.11]^10 - 1 )/0.11
FV= $5,300 * 16.722008965
FV= $88,626.647515
This implies our parents will have the above amount when Linda is to start college and will require an additional $43,373.35248 ($132,000 - $88,626.647515 ) to have the entire fees at hand.
Now, we have to determine how much should be saved every year for the next five years (when Linda starts school) in order to obtain the amount left to complete Linda's fees.
Considering the formula above, it should be noted that we alraedy know the future value, the interest and the number of years involved. So to get the cash flow or amount to be saved per period,
- Cash Flow per period C = Future value FV/ ([1 + i]^n - 1 )/i
C = $43,373.35248 / ([1 + 0.11]^5 - 1 )/0.11
C = $43.373.35248 / 6.22780141
C = $6,964.4726324
Thus, in addition to the $5,300 currently being saved by our parents, they will have to save an additional $6,964.4726324 per year so as to obtain the total amount for Linda fees of $132,000 which will be divided into $33,000 per year.
