Question

The National Science Foundation (NSF) offers grants to students who are interested in pursuing a college education. The student must be enrolled full time (12 credit hours or more), and hold a grade point average of 3.8. The NSF will pay $9,500 per year towards tuition for 4 years. The initial amount is placed into an account paying 7.8% compounded annually, and the tuition is drawn from the account until the remaining balance is zero dollars. Determine the initial amount invested by the NSF. Round your answer to the nearest dollar.
a.
$30,000
c.
$35,036
b.
$31,606
d.
$38,000

Answer 1

PVAO=9500[(1-(1+0.078)^(-4))/0.078]
PVAO=31605.79
So the answer is 31606

Answer 2

Answer:

The answer is option b.  $31,606

Step-by-step explanation:

The NSF will pay $9,500 per year towards tuition for 4 years.

So, p = 9500

r = 7.8% or 0.078

t = 4

We can find the initial amount invested by:

$p(\frac{1-(1+r)^{-t} }{r})$

Putting values in the formula we get

$9500(\frac{1-(1.078)^{-4} }{0.078} )$

$9500(\frac{1-0.74050}{0.078} )$

= $31605.769

Rounding this to nearest whole number, we get $31606.

So, option B is the correct answer.