Question

Problem 4-10
Present and Future Values of Single Cash Flows for Different Interest Rates

Use both the TVM equations and a financial calculator to find the following values. Round your answers to the nearest cent. (Hint: 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 parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

1. An initial $200 compounded for 10 years at 6.7 percent.
   $   
   
2. An initial $200 compounded for 10 years at 13.4 percent.
   $   
   
3. The present value of $200 due in 10 years at a 6.7 percent discount rate.
   $   
   
4. The present value of $200 due in 10 years at a 13.4 percent discount rate.
   $  

Answer 1

In order to compute the future value of an investment we shall use the below equation:

Future Value = Present Value x ( 1 + discount rate )ⁿ

In parts a and b we shall use the above equation to compute the future value:

a. Following are the values that we will plug in the above equation:

Present Value = $ 200

N = 10 years

I/Y = 6.7% or 0.067 (Discount rate)

Future Value = 200 x ( 1 + 0.067 ) ¹⁰

= $ 382.54

By using the financial calculator the above solution can be arrived by plugging the below figures in the calculator:

PV = 200

PMT = 0 (Since no payment is there in the question)

N = 10

I/Y = 6.7

Compute FV, which will give the same value as we computed above i.e. $ 382.54

b. Following are the values that we will plug in the above equation:

Present Value = $ 200

N = 10 years

I/Y = 13.4% or 0.134 (Discount rate)

Future Value = 200 x ( 1 + 0.134 ) ¹⁰

= $ 703.33

By using the financial calculator the above solution can be arrived by plugging the below figures in the calculator:

PV = 200

PMT = 0 (Since no payment is there in the question)

N = 10

I/Y = 13.4

Compute FV, which will give the same value as we computed above i.e. $ 703.33

In order to compute the present value of an investment we shall use the below equation:

Present Value = Future Value / ( 1 + discount rate )ⁿ

In parts c and d we shall use the above equation to compute the present value:

c. Following are the values that we will plug in the above equation:

Future Value = $ 200

N = 10 years

I/Y = 6.7% or 0.067 (Discount rate)

Present Value = 200 / ( 1 + 0.067 ) ¹⁰

= $ 104.56

By using the financial calculator the above solution can be arrived by plugging the below figures in the calculator:

FV = 200

PMT = 0 (Since no payment is there in the question)

N = 10

I/Y = 6.7

Compute PV, which will give the same value as we computed above i.e. $ 104.56.

d. Following are the values that we will plug in the above equation:

Future Value = $ 200

N = 10 years

I/Y = 13.4% or 0.134 (Discount rate)

Present Value = 200 / ( 1 + 0.134 ) ¹⁰

= $ 56.87

By using the financial calculator the above solution can be arrived by plugging the below figures in the calculator:

FV = 200

PMT = 0 (Since no payment is there in the question)

N = 10

I/Y = 13.4

Compute PV, which will give the same value as we computed above i.e. $ 56.87.

Feel free to ask in case of any queries regarding this question