Question

Suppose you are going to receive $21,500 per year for five years. The appropriate interest rate is 7 percent.

a-1.	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?

Answer 1

Information provided:

Annuity= $21,500

Time= 5 years

Interest rate= 7%

a.1. Ordinary Annuity refers to an annuity that occurs at the end of the period.

The present value of ordinary annuity can be computed by entering the below in a financial calculator:

PMT= 21,500

N= 5

I/Y= 7

Press the CPT key and PV to compute the present value of ordinary annuity.

The value obtained is 88,154.24.

Therefore, the present value of ordinary annuity is $88,154.24.

a.2.Annuity due refers to annuity that occurs at the beginning of a period.

This can be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^nd BGN 2^nd SET on the Texas BA II Plus calculator.

The present value of annuity due can be computed by entering the below in a financial calculator in BGN mode:

PMT= 21,500

N= 5

I/Y= 7

Press the CPT key and PV to compute the present value of ordinary annuity.

The value obtained is 94,325.04.

Therefore, the present value of ordinary annuity is $94,325.04.

b-1. The future value of ordinary annuity refers to an annuity that occurs at the end of the period.

The future value of ordinary annuity can be computed by entering the below in a financial calculator:

PMT= 21,500

N= 5

I/Y= 7

Press the CPT key and FV to compute the present value of ordinary annuity.

The value obtained is 123,640.89.

Therefore, the future value of ordinary annuity is $123,640.89.

b-2. Annuity due refers to annuity that occurs at the beginning of a period.

This can be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^nd BGN 2^nd SET on the Texas BA II Plus calculator.

The future value of annuity due can be computed by entering the below in a financial calculator in BGN mode:

PMT= 21,500

N= 5

I/Y= 7

Press the CPT key and FV to compute the present value of ordinary annuity.

The value obtained is 132,295.75.

Therefore, the future value of ordinary annuity is $132,295.75.

c-1.Annuity due has a higher present value. The reason being that in annuity due the payments are made at the beginning of the period, an annuity due has a higher value than an ordinary annuity.

c-2.Annuity due has a higher future value. The reason being that in annuity due the payments are made at the beginning of the period, an annuity due has a higher value than an ordinary annuity.

In case of any query, kindly comment on the solution.