Question

What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a-2. What is the present value of the payments if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-1. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-2. What is the future value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c-1. Which has the higher present value, the ordinary annuity or annuity due? c-2. Which has the higher future value? 13500

Answer 1

Suppose you are going to receive $10,000 per year for five years. The appropriate interest rate is 11 percent.

answer-

Requirement 1: a)

Present Value Annuity = 10000 x { 1 - 1/(1 + 0.11)^5 }/0.11

= 10000 x { 1 - 1/(1.11)^5 }/0.11

= 10000 x { 1 - 1/1.6850581551 }/0.11

= 10000 x { 1 - 0.593451328059 }/0.11

= 10000 x 0.406548671941/0.11

= 10000 x 3.69589701765

Present Value Annuity = 36958.97

Requirement 1: b)

Present Value Annuity Due = 10000 x (1 + 0.11) x { 1 - 1/(1 + 0.11)^5 }/0.11

= 10000 x 1.11 x { 1 - 1/(1.11)^5 }/0.11

= 10000 x 1.11 x { 1 - 1/1.6850581551 }/0.11

= 10000 x 1.11 x { 1 - 0.593451328059 }/0.11

= 10000 x 1.11 x { 0.406548671941/0.11 }

= 10000 x 1.11 x 3.69589701765

= 10000 x 4.10244568959

Present Value Annuity Due = 41024.46

Requirement 2: a)

Future Value Annuity = 10000 x { (1 + 0.11)^5 - 1 }/0.11

= 10000 x { (1.11)^5 - 1 }/0.11

= 10000 x { 1.6850581551 - 1 }/0.11

= 10000 x 0.6850581551/0.11

= 10000 x 6.22780141

Future Value Annuity = 62278.01

Requirement 2: b)

Future Value Annuity Due = 10000 x (1 + 0.11){ (1 + 0.11)^5 - 1 }/0.11

= 10000 x 1.11 x { (1.11)^5 - 1 }/0.11

= 10000 x 1.11 x { 1.6850581551 - 1 }/0.11

= 10000 x 1.11 x 0.6850581551/0.11

= 10000 x 1.11 x 6.22780141

= 10000 x 6.9128595651

Future Value Annuity Due = 69128.6