1) Computation of the percentage of students who received a merit scholarship:-

X = 4,200

Mean = 3,449

Standard deviation = 466

P(X<4200)=P((X-mean)/Standard deviation < (4200-3449)/466)

P(X< 4200) = P(Z<1.61)

=0.9463 (From z-table)

= 94.63%

 

 

2) Computation of the purchase price of property:-

First we calculate the present value of annuity ;

PV of annuity = Annuity*((1-1/(1+rate)^n)/rate)

Here, rate = 5.12% / 2 = 2.56% (semiannual)

n = 6*2 = 12 periods (semiannual)

PV of annuity = $1147*((1-1/(1+2.56%)^12)/2.56%)

= $1147*10.12278

= $11,724.38

Purchase price = Down payment + PV of annuity

= $8,404 + $11,724.38

= $20,128.38

Working note:-

EAR = (1+rate/n)^n-1

= (1+5%/12)^12-1

= 1.0512 - 1

= 5.12%

Computation of the cost of financing:-

Cost of financing = Total payment - PV of annuity

= ($1147*6*2) - $11,724.38

= $13,764 - $11,724.38

= $2,039.62