[I’M DOING THE STANDARD PAYMENT] 1) You borrow $61,200 to attend college, and will repay your loan at 3.6% APR. Calculate…
a. Your monthly repayment if you choose standard repayment..
c. Your total repayment if you choose standard repayment.
e. The amount of interest repaid if you choose standard repayment.
g. How much money will you save by electing standard repayment?

Show your work on how you got your answer

9514 1404 393

  a) $608.05

  c) $72,966

  e) $11,766

  g) $19,935

Step-by-step explanation:

The formula for the monthly payment amount on a loan of P at rate r for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

For the standard repayment plan, t = 10. You have P = $61,200 and r = 0.036, so the formula becomes ...

  A = $61,200(0.036/12)/(1 -(1 +0.036/12)^(-12·10))

  = $61,200(0.003)/(1 -1.003^-120)

  = $608.05

a) The monthly payment under the standard repayment plan is $608.05.

__

c) The total of 12 payments per year over 10 years is ...

  $608.05×10×12 = $72,966.00

__

e) The interest paid is the difference between payments and the amount borrowed:

  interest = $72,966 -61,200 = $11,766

__

g) Payments under the extended repayment plan last for 25 years (300 months). They will be $309.67 (found using a financial calculator). The total of those payments will be $309.67×300 = $92,901. Your savings under the standard plan are ...

  $92,901 -72,966 = $19,935

Additional comment

Many graphing calculators have apps for figuring loan payments or other parameters. Spreadsheets have these functions, too.

Here, we have rounded the loan payment value to the nearest cent. This means the payment differs slightly from the computed value. In the real world, the final loan payment will be different from the rest, so as to take care of this discrepancy. In addition to the unpaid principal, there will be an interest charge that depends on the precise day on which the final payment is made.

We're never quite sure how accurate the answer is expected to be, so we've done the calculations using the loan payment value we came up with.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.