i. ( A / F , i , n ) = ( A / P , i , n ) − i .

Question

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Answer 1

Question

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

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Answer 2

Question

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

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Answer 3

Question

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

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Answer 4

Question

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

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Answer 5

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

Answer 6

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

Answer 7

Chapter 4, Problem 51P

To determine

i.

(A/F,i,n) = (A/P,i,n)−i.

Answer 8

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

(A/F,i,n) = (A/P,i,n)−i.

Calculation:

The following relationship is required to be proved:

(A/F,i,n) = (A/P,i,n) − i..................(1)

Take the right-side of the equation (1) and simplify it into the left side of the equation.

Right-hand side = (A/P,i,n) − i

Right hand side = i(1+i)n(1+i)n− 1−i

Right hand side = i(1+i)n −i[(1+i)n−1](1+i)n− 1

Right hand side = i(1+i)n− 1

Right hand side = (A/F,i,n).

Conclusion:

Right hand side = Left hand side.

Answer 13

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

Answer 14

To determine

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Answer 15

Expert Solution

Answer to Problem 51P

Left hand side = Right hand side.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Calculation:

The following relationship is required to be proved:

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1)..........(2)

Right hand side = (P/A,i,n)−(P/A,i,n−1)

Right hand side = i(1+i)n(1+i)n− 1−(1+i)n−1−1i(1+i)n−1

Right hand side = i(1+i)n −1(1+i)n−(1+i)n−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−1i(1+i)n(1+i)−1

Right hand side = (1+i)−1(1+i)n−(1+i)−1−[( 1+i)n−1−1]i(1+i)n(1+i)−1

Right hand side = (1+i)n−1(1+i)−1−(1+i)n−1+1i(1+i)n(1+i)−1

Right hand side = 1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1i(1+i)n(1+i)−1−(1+i)−1i(1+i)n(1+i)−1

Right hand side = 1+i−1i(1+i)n

Right hand side = ii(1+i)n

Right hand side = 1(1+i)n

Right hand side = (1+i)−n

Right hand side = (P/F,i,n).

Conclusion:

Right hand side = Left hand side.

Answer 20

Ch. 4 - Prob. 1QTC Ch. 4 - Prob. 2QTC Ch. 4 - Prob. 3QTC Ch. 4 - Prob. 4QTC Ch. 4 - Prob. 5QTC Ch. 4 - Prob. 1P Ch. 4 - Prob. 2P Ch. 4 - Prob. 3P Ch. 4 - Prob. 4P Ch. 4 - Prob. 5P

i. ( A / F , i , n ) = ( A / P , i , n ) − i .

i. (A/F,i,n) = (A/P,i,n)−i.

Answer to Problem 51P

Explanation of Solution

ii. (P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).

Answer to Problem 51P

Explanation of Solution

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Chapter 4 Solutions

i.

(A/F,i,n) = (A/P,i,n)−i.

ii.

(P/F,i,n) = (P/A,i,n)−(P/A,i,n−1).