Question

Problem 4-17
Present Value for Various Compounding Periods

Find the present value of $475 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

1. 12% nominal rate, semiannual compounding, discounted back 5 years
   $  
   
2. 12% nominal rate, quarterly compounding, discounted back 5 years
   $  
   
3. 12% nominal rate, monthly compounding, discounted back 1 year
   $  

Answer 1

a.Information provided:

Future value= $475

Time= 5 years*2= 10 semi-annual periods

Interest rate= 12%/2= 6% per semi-annual periods

Enter the below in a financial calculator to compute the present value:

FV= 475

N= 10

I/Y= 6

Press the CPT and PV to compute the present value.

The value obtained is 265.24.

Therefore, the present value is $265.24.

b.Information provided:

Future value= $475

Time= 5 years*4= 20 quarters

Interest rate= 12%/4= 3% per quarter

Enter the below in a financial calculator to compute the present value:

FV= 475

N= 10

I/Y= 3

Press the CPT and PV to compute the present value.

The value obtained is 262.9960

Therefore, the present value is $263.

c. Information provided:

Future value= $475

Time= 5 years*12= 60 months

Interest rate= 12%/12= 1% per month

Enter the below in a financial calculator to compute the present value:

FV= 475

N= 60

I/Y= 1

Press the CPT and PV to compute the present value.

The value obtained is 261.46

Therefore, the present value is $261.46.

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