Question

Your younger sister, Linda, will start college in five years. She has just informed your parents that she wants to go to Hampton University, which will cost $33,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda’s ambitions, your parents started investing $5,300 per year five years ago and will continue to do so for five more years. Use 11 percent as the appropriate interest rate throughout this problem (for discounting or compounding).How much will your parents have to save each year for the next five years in addition to the $5,300 they are currently saving to have the necessary funds for Linda's education? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)My answer is 2206.07 and I've solved it a billion times and it still says its wrong. Please enlighten me.

Answer 1

Answer: = $2208.49

Explanation:

Value of college fee at end of year 5

= PVA 11%,4*Cost

= 3.10245*33000

= $102380.71

Value of investment made five year ago at end of year 5

= FVA 11%,10* Investment amount

= 16.72201 * 5300

= $88626.65

∴Amount of additional investment required

⇒ 102380.71 - 88626.65 = 13754.06

Amount of investment required per year for 5 years

= Additional investment /FVA11%,5

= 13754.06 / 6.22780

= $2208.49

Answer 2

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.