Question

Your younger sister, Barbara, will start college in five years. She has just informed your parents that she wants to go to Eastern University, which will cost $38,000 per year for four years (assumed to come at the end of each year). Anticipating Barbara’s ambitions, your parents started investing $2,000 per year five years ago and will continue to do so for five more years. Use 12 percent as the appropriate interest rate throughout this problem. Barbara is now 18 years old (five years have passed), and she wants to get married instead of going to school. Your parents have accumulated the necessary funds for her education.

Instead of her schooling, your parents are paying $18,000 for her upcoming wedding and plan to take a year-end vacation costing $11,000 per year for the next 3 years.(Use a Financial calculator to arrive at the answers.)

a. How much will your parents have at the end of 3 years to help you with graduate school, which you will start then? (Round the final answer to the nearest whole dollar.)

b. You plan to work on a master’s and perhaps a Ph.D. If graduate school costs $57,451 per year, approximately how long will you be able to stay in school based on these funds?(Round the final answer to the nearest whole year.)

Number of year

Answer 1

Answer-a

College cost = $38000 per year for 4 years .

interest rate = 12%.

henec PV of the College fees at the beginning of college = Annual Cash flow* [ 1- (1/ (1+r)^n ] / r

=>PV of the College fees at the beginning of college = $38000*[1-(1/(1.12)^4]/0.12 = $115419

As the question has given that the parent has accumulated all the necesary funds , hence now the the value of the Investment is $115419.

hence your parents will have $99749 at the end of 3 years to help you with graduate school, which you will start then

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Answer-b

Let the number of year you will be able to stay based on these funds be ''n'' years

As we know,

Prsent value of Annuity =Annual Cash flow* [ 1- (1/ (1+r)^n ] / r

=.>value at year end 3 = Annual cost*[ 1- (1/ (1+r)^n ] / r

=>$99749 = $57451* [1-(1/(1.12)^t]/0.12

=>1-(1/(1.12)^n) = 0.208349

=>1/ (1.12)^n = 0.791651

=>1.12^n = 1.263183

=> n = 2.0616 Year, or 2 year

By excel,

Present value after 3 yaer (PV)	$99,749
Annual payment (PMT)	$57,451
Iinterest rate	12%
Number of period (NPER)	2.0616 or 2 year	=NPER(12%,-57451,99749,0,0)
		=NPER(rate, payment_amount, present_value, [future_value], [end_or_beginning])