Suppose you are going to receive $14,000 per year for five years. The appropriat

Question

Suppose you are going to receive $14,000 per year for five years. The appropriate interest rate is 7 percent.

What is the present value of the payments if they are in the form of an ordinary annuity? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations.Round your answer to 2 decimal places (e.g., 32.16).)

What is the present value of the payments if the payments are an annuity due? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

What is the future value if the payments are an annuity due? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

What is the present value of the payments if they are in the form of an ordinary annuity? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations.Round your answer to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Requirement 1

a)

Present Value Annuity = 14000 x { 1 - 1/(1 + 0.07)^5 }/0.07
= 14000 x { 1 - 1/(1.07)^5 }/0.07
= 14000 x { 1 - 1/1.402551731 }/0.07
= 14000 x { 1 - 0.7129861795 }/0.07
= 14000 x 0.2870138205/0.07
= 14000 x 4.100197436
Present Value Annuity = 57402.7641

=57402.76 $

b)

Present Value Annuity Due = 14000 x (1 + 0.07) x { 1 - 1/(1 + 0.07)^5 }/0.07
= 14000 x 1.07 x { 1 - 1/(1.07)^5 }/0.07
= 14000 x 1.07 x { 1 - 1/1.402551731 }/0.07
= 14000 x 1.07 x { 1 - 0.7129861795 }/0.07
= 14000 x 1.07 x {0.2870138205/0.07 }
= 14000 x 1.07 x 4.100197436
Present Value Annuity Due = 61420.95759

=61420.95 $

Requirement 2

a)

Future Value Annuity = 14000 x { (1 + 0.07)^5 - 1 }/0.07
= 14000 x { (1.07)^5 - 1 }/0.07
= 14000 x { 1.402551731 - 1 }/0.07
= 14000 x 0.402551731/0.07
= 14000 x 5.750739014
Future Value Annuity = 80510.3462

=80510.34 $

b)

Future Value Annuity Due = 14000 x (1 + 0.07){ (1 + 0.07)^5 - 1 }/0.07
= 14000 x 1.07 x { (1.07)^5 - 1 }/0.07
= 14000 x 1.07 x { 1.402551731 - 1 }/0.07
= 14000 x 1.07 x0.402551731/0.07
= 14000 x 1.07 x 5.750739014

Future Value Annuity Due = 86146.07043

=86146.07 $

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