Say you are considering two loans. Loan F has a nominal interest rate of 5.66%, compounded monthly. Loan G has a rate of 6.02%, compounded semiannually. Which loan will give the lower effective interest rate, and how much lower will it be? A) Loan G's effective rate will be 0.091 percentage points lower than Loan F's
B) Loan G's effective rate will be 0.058 percentage points lower than Loan F's
C) Loan F's effective rate will be 0.302 percentage points lower than Loan G's
D) Loan F's effective rate will be 0.149 percentage points lower than Loan G's

C) Loan F's effective rate will be 0.302 percentage points lower than Loan G's

Step-by-step explanation:

Formula for effective rate is;

r_eff = [1 + (r/n)]^(n) - 1

Where;

r is interest rate

n is the number of compounding periods per year

Loan F has a nominal interest rate of 5.66%, compounded monthly

Thus: r_eff = [1 + (0.0566/12)]^(12) - 1 = 0.0581

Loan G has a rate of 6.02%, compounded semiannually.

Thus;

r_eff = [1 + (0.0602/2)]^(2) - 1 = 0.0611

Differece = 0.0611 - 0.0581 = 0.003

Converting to percentage gives : 0.003 × 100 = 0.3%

Thus,correct answer is option C

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240