Question

Problem 4-12
Future Value of an Annuity

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

1. $400 per year for 10 years at 12%.
   $   
   
2. $200 per year for 5 years at 6%.
   $   
   
3. $400 per year for 5 years at 0%.
   $  

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

4. $400 per year for 10 years at 12%.
   $   
   
5. $200 per year for 5 years at 6%.
   $   
   
6. $400 per year for 5 years at 0%.
   $  

Answer 1

1.a. Information provided:

Annual payment= $400

Time= 10 years

Interest rate= 12%

The future value is calculated by entering the below in a financial calculator:

PMT= 400

N= 10

I/Y= 12

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

The value obtained is 7,019.49.

Therefore, the future value of the annuity is $7,019.49.

b. Information provided:

Annual payment= $200

Time= 5 years

Interest rate= 6%

The future value is calculated by entering the below in a financial calculator:

PMT= 200

N= 5

I/Y= 6

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

The value obtained is 1,127.42.

Therefore, the future value of the annuity is $1,127.42.

c. Information provided:

Annual payment= $400

Time= 5 years

Interest rate= 0%

The future value is calculated by entering the below in a financial calculator:

PMT= 400

N= 5

I/Y= 0

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

The value obtained is 2,000.

Therefore, the future value of the annuity is $2,000.

2.a. Information provided:

Annual payment= $400

Time= 10 years

Interest rate= 12%

The question is concerning finding the future value of an annuity due. 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 future value is calculated by entering the below in a financial calculator in BGN mode:

PMT= 400

N= 10

I/Y= 12

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

The value obtained is 7,861.83.

Therefore, the future value of the annuity is $7,861.83.

b.Information provided:

Annual payment= $200

Time= 5 years

Interest rate= 6%

The future value is calculated by entering the below in a financial calculator in BGN mode:

PMT= 200

N= 5

I/Y= 6

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

The value obtained is 1,195.06.

Therefore, the future value of the annuity is $1,195.06.

c.Information provided:

Annual payment= $400

Time= 5 years

Interest rate= 0%

The question is concerning finding the future value of an annuity due. 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 future value is calculated by entering the below in a financial calculator in BGN mode:

PMT= 400

N= 5

I/Y= 0

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

The value obtained is 2,000.

Therefore, the future value of the annuity is $2,000.

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