Question

PRESENT VALUE OF AN ANNUITY

Find the present values of these ordinary annuities. Discounting occurs once a year. Round your answers to the nearest cent.

1. $700 per year for 16 years at 6%.

   $  

2. $350 per year for 8 years at 3%.

   $  

3. $800 per year for 6 years at 0%.

   $  

   Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

4. $700 per year for 16 years at 6%.

   $  

5. $350 per year for 8 years at 3%.

   $  

6. $800 per year for 6 years at 0%.

   $  

Answer 1

a.Information provided:

Annuity= $700

Time= 16 years

Interest rate= 6%

The present value of ordinary annuity is computed by entering the below in a financial calculator in the default END mode:

PMT= 700

N= 16

I/Y= 6

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

The value obtained is 7,074.13.

Therefore, the present value of ordinary annuity is $7,074.13.

b. Information provided:

Annuity= $350

Time= 8 years

Interest rate= 3%

The present value of ordinary annuity is computed by entering the below in a financial calculator in the default END mode:

PMT= 350

N= 8

I/Y= 3

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

The value obtained is 2,456.89.

Therefore, the present value of ordinary annuity is $2,456.89.

c. Information provided:

Annuity= $800

Time= 6 years

Interest rate= 0%

The present value of ordinary annuity is computed by entering the below in a financial calculator in the default END mode:

PMT= 800

N= 6

I/Y= 0

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

The value obtained is 4,800.

Therefore, the present value of ordinary annuity is $4,800.

d. Information provided:

Annuity= $700

Time= 16 years

Interest rate= 6%

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^nd BGN 2^nd SET on the Texas BA II Plus calculator.

The present value of annuity due is computed by entering the below in a financial calculator in the default END mode:

PMT= 700

N= 16

I/Y= 6

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

The value obtained is 7,498.57.

Therefore, the present value of annuity due is $7,498.57.

e. Information provided:

Annuity= $350

Time= 8 years

Interest rate= =3%

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^nd BGN 2^nd SET on the Texas BA II Plus calculator.

The present value of annuity due is computed by entering the below in a financial calculator in the default END mode:

PMT= 350

N= 8

I/Y= 3

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

The value obtained is 2,530.60.

Therefore, the present value of annuity due is $2,530.60.

f. Information provided:

Annuity= $800

Time= 6 years

Interest 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^nd BGN 2^nd SET on the Texas BA II Plus calculator.

The present value of annuity due is computed by entering the below in a financial calculator in the default END mode:

PMT= 800

N= 6

I/Y= 0

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

The value obtained is 4,800.

Therefore, the present value of annuity due is $4,800.

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