Question

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $1,000 per year for 14 years at 4%.

   $  

2. $500 per year for 7 years at 2%.

   $  

3. $700 per year for 7 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $1,000 per year for 14 years at 4%: $  

   Present value of $500 per year for 7 years at 2%: $  

   Present value of $700 per year for 7 years at 0%: $  

Answer 1

a.Information provided:

Annuity= $1,000

Time= 14 years

Discount rate= 4%

Ordinary annuity refers to the annuity which occurs at the end of the period. The present value of an ordinary annuity can be computed with the help of a financial calculator.

The calculator by default is the END mode which is needed to calculate ordinary annuity values. The future value can be computed by entering the below:

PMT= 1,000

N= 14

I/Y= 4

Press the CPT key and PV to calculate the present value.

The value obtained is 10,563.12.

Therefore, the present value is $10,563.12.

b.Information provided:

Annuity= $500

Time= 7 years

Discount rate= 2%

Ordinary annuity refers to the annuity which occurs at the end of the period. The present value of an ordinary annuity can be computed with the help of a financial calculator.

The calculator by default is the END mode which is needed to calculate ordinary annuity values. The future value can be computed by entering the below:

PMT= 500

N= 7

I/Y= 2

Press the CPT key and PV to calculate the present value.

The value obtained is 3,236.

Therefore, the present value is $3,236.

c.Information provided:

Annuity= $700

Time= 7 years

Discount rate= 0%

Ordinary annuity refers to the annuity which occurs at the end of the period. The present value of an ordinary annuity can be computed with the help of a financial calculator.

The calculator by default is the END mode which is needed to calculate ordinary annuity values. The future value can be computed by entering the below:

PMT= 700

N= 7

I/Y= 0

Press the CPT key and PV to calculate the present value.

The value obtained is 4,900.

Therefore, the present value is $4,900.

d.i.Information provided:

Annuity= $1,000

Time= 14 years

Discount rate= 4%

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

This can also 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^ndBGN 2^ndSET on the Texas BA II Plus calculator.

The question can also be solved using a financial calculator by entering the below into the calculator now:

PMT= 1,000

N= 14

I/Y= 4

Press the CPT key and PV to calculate the present value.

The value obtained is 10,985.65.

Therefore, the present value is $10,985.65.

ii.Information provided:

Annuity= $500

Time= 7 years

Discount rate= 2%

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

This can also 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^ndBGN 2^ndSET on the Texas BA II Plus calculator.

The question can also be solved using a financial calculator by entering the below into the calculator now:

PMT= 500

N= 7

I/Y= 2

Press the CPT key and PV to calculate the present value.

The value obtained is 3,300.72.

Therefore, the present value is $3,300.72.

c.Information provided:

Annuity= $700

Time= 7 years

Discount rate= 0%

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

This can also 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^ndBGN 2^ndSET on the Texas BA II Plus calculator.

The question can also be solved using a financial calculator by entering the below into the calculator now:

PMT= 700

N= 7

I/Y= 0

Press the CPT key and PV to calculate the present value.

The value obtained is 4900.

Therefore, the present value is $4,900.