Eric deposits X into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually. Mike deposits 2X into a different savings account at time 0, which pays simple interest at an annual rate of i. Eric and Mike earn the same amount of interest during the last 6 months of the 8th year. Calculate i.

i = 9.46%

Step-by-step explanation:

Money deposited by Eric is X.

Now formula for compound interest is;

A = P(1 + i)ⁿ

Where n = kt and k is the number of compounding per annum.

Since Eric compounded interest semi annually, we have;

A = X(1 + i/2)^(2t)

After 7.5 years, Eric will earn;

A(7.5) = X(1 + i/2)^(2 * 7.5)

A_7.5 = X(1 + i/2)^(15)

For the last half year, where n = 1, Eric earns; (A_7.5)(1 + i/2)¹

Thus, the interest eric earns = (A_7.5)(1 + i/2) - A_7.5

Interest = A_7.5 + (A_7.5)*(i/2) - A_7.5

Interest = (A_7.5)*(i/2)

We initially got A_7.5 = X(1 + i/2)^(15)

Thus, interest Eric earns is now ;

X(1 + i/2)^(15) * (i/2)

Which gives;

0.5Xi(1 + i/2)^(15)

Now to mike. He deposited 2X

Simple interest earned by mike will be;

A = 2X(1 + it)

During the last half year of any yeat, Mike earns; 2X * i/2 = Xi

Equating last half year interests of both Eric and Mike gives us;

0.5Xi(1 + i/2)^(15) = Xi

Divide both sides by 0.5Xi to give;

(1 + i/2)^(15) = 2

So,

1 + i/2 = 2^(1/15)

i/2 = 1.04729 - 1

i/2 = 0.04729

Multiply both sides by 2 to give;

i = 0.09458

Thus, interest is approximately 0.0946 or 9.46%

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841