Mike is looking for a loan. he is willing to pay no more than an effective rate of 8.000% annually. which, if any, of the following loans meet mike’s criteria?
loan x: 7.815% nominal rate, compounded semiannually
loan y: 7.724% nominal rate, compounded monthly
loan z: 7.698% nominal rate, compounded weekly
a. y only
b. x and z
c. y and z
d. none of these meet mike’s criteria.

b. X and Z

Step-by-step explanation:

Since, the effective annual rate is,

Where r is the nominal rate per period,

m is the number of periods in a year,

For loan X,

r = 7.815 % = 0.07815

m = 2,

Thus, the effective annual rate,

Since, 7.968\% < 8.000 %

Thus, Loan X meets his criteria.

For loan Y,

r = 7.724%= 0.07724

m = 12,

Thus, the effective annual rate,

Since, 8.003 > 8.000 %

Thus, Loan Y does not meet his criteria.

For loan Z,

r = 7.698% = 0.07698

m = 52,

Thus, the effective annual rate,

Since, 7.996 % < 8.000 %

Thus, Loan Z meets his criteria.

Hence, option 'b' is correct.

4

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11