On January 1, 1980, Jack deposited 1,000 into Bank X to earn interest at the rate of j per annum compounded semi-annually. On January 1, 1985, he transferred his account to Bank Y to earn interest at the rate of k per annum compounded quarterly. On January 1, 1988, the balance at Bank Y is 1,990.76. If Jack could have earned interest at the rate of k per annum compounded quarterly from January 1, 1980 through January 1, 1988, his balance would have been 2,203.76. Calculate the ratio kjkj.

Ratio k/j is 1.25.

Explanation:

Note: There is a slight typographical error in the requirement. The requirement is therefore correctly stated as follows:

Calculate the ratio k/j.

The explanation of the answer is given as follows:

This can be calculated using the following formula:

A = P (1 + (r / m))^(tm) ……………………….. (1)

Where;

A = Balance

P = Amount invested

r = annual interest rate

t = number of years

m = number of compounding

From the question, there are 2 alternatives as follows:

Alternative A

For Bank X

P1 = $1,000

r1 = j

t1 = number of years from 1980 to 1985 = 5

m1 = semiannual = 2

A1 = Amount transferred to Bank Y = P2 = ?

For Bank Y

P2 = ?

r2 = k

t2 = number of years from 1985 to 1988 = 3

m2 = quarterly = 4

A2 = $1,990.76

Alternative B

For Bank Y only

P3 = $1,000

r3 = k

t3 = number of years from 1980 to 1988 = 8

m3 = quarterly = 4

A3 = $2,203.76

For Bank Y in alternative B, we can use equation (1) and solve for k as follows:

2,203.76 = 1000 * (1 + (k / 4))^(8 * 4)

2,203.76 / 1000 = (1 + (k / 4))^32

2.20376 = (1 + (k / 4))^32

2.20376^(1/32) = 1 + (k / 4)

1.02500004450895 = 1 + (k / 4)

1.02500004450895 - 1 = k / 4

0.02500004450895 = k / 4

k = 0.02500004450895 * 4

k = 0.10

For Bank Y in alternative A, we can use r2 = k = 0.10. Therefore, using equation (1) for Bank Y in alternative A, we can solve for P2 as follows:

1,990.76 = P2 * (1 + (0.10 / 4))^(3 * 4)

1,990.76 = P2 * 1.3448888242463

P2 = 1,990.76 / 1.3448888242463

P2 = $1,480.24

From Bank X in alternative A, we now have A1 = P2 = $1,480.24. For Bank X in alternative A, we can now use equation (1) and solve for j as follows:

1,480.24 = 1,000 (1 + (j / 2))^(5 * 2)

1,480.24 / 1,000 =(1 + (j / 2))^10

1.480.24 =(1 + (j / 2))^10

1.480.24^(1 / 10) = 1 + (j / 2)

1.03999969894693 - 1 = j / 2

0.03999969894693 = j / 2

j = 0.03999969894693 * 2

j = 0.08

Since k = 0.10 and j = 0.08, ratio k/j can be calculated as follows:

Ratio k/j = 0.10 / 0.08

Ratio k/j = 1.25

answer; tech (a) is correct;

whole quiz

1. the sum of all activities involved in getting high-quality products into the marketplace

2.operations

3. the principle of looking at the supply chain as a whole in order to improve the overall flow through the system.

4. produced; performed

5. activities producing tangible products, such as radios, newspapers, buses, and textbooks.

6. activities producing intangible and tangible products, such as entertainment, transportation, and education.

7.   customer focus

8. analyzing a competitor's products to identify desirable improvements

9. the systematic direction and control of the processes that transform resources into finished projects that create value for and provide benefits to consumers.

10. operation management.

your welcome leave a rate and a < 3