Question

Compute the present value of a $500 investment made 6 months, 5 years, and 10 years from now at 6 percent interest. (Remember the exponent for the 6 month calculation is expressed as 0.5, representing one-half of one year.)

Instructions: Enter your responses to the nearest penny (2 decimal places). Do not round intermediate calculations.

Present value of investment made in 6 months at 6 percent = $

Present values of investment made in 5 years at 6 percent = $

Present value of investment made in 10 years at 6 percent = $

Answer 1

Solution:

1. Calculation of Present value of investment of $ 500 made in 6 months at 6 percent :

The present value of an Investment made at period 'n' is calculated using the following formula:

PV = C_n / (1 + r )ⁿ

Where PV = Present Value   ; C_n : Amount of Investment made at period n ;

r = Interest rate ; n = Number of periods or years ;

As per the information given in the question we have

r = 6 % = 0.06   ; n = 6 months = 0.5 years   ;    C_0.5 = $ 500 ;

Applying the above values in the formula we have

PV = $ 500 / ( 1 + 0.06 ) ^0.5

= $ 500 / ( 1.06 ) ^0.5

= $ 500 / 1.029563

= $ 485.642931

= $ 485.64 ( When rounded off to two decimal places )

Thus the Present value of investment of $ 500 made in 6 months at 6 percent = $ 485.64

Note : The value of ( 1.06 ) ^0.5   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.06,0.5) = 1.029563

2. Calculation of Present values of investment of $ 500 made in 5 years at 6 percent :

The present value of an Investment made at period 'n' is calculated using the following formula:

PV = C_n / (1 + r )ⁿ

Where PV = Present Value   ; C_n : Amount of Investment made at period n ;

r = Interest rate ; n = Number of periods or years ;

As per the information given in the question we have

r = 6 % = 0.06   ; n = 5 years   ;    C₅ = $ 500 ;

Applying the above values in the formula we have

PV = $ 500 / ( 1 + 0.06 ) ⁵

= $ 500 / ( 1.06 ) ⁵

= $ 500 / 1.338226

= $ 373.629086

= $ 373.63 ( When rounded off to two decimal places )

Thus the Present value of investment of $ 500 made in 5 years at 6 percent = $ 373.63

Note : The value of ( 1.06 ) ⁵   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.06,5) = 1.338226

3. Calculation of Present value of investment of $ 500 made in 10 years at 6 percent :

The present value of an Investment made at period 'n' is calculated using the following formula:

PV = C_n / (1 + r )ⁿ

Where PV = Present Value   ; C_n : Amount of Investment made at period n ;

r = Interest rate ; n = Number of periods or years ;

As per the information given in the question we have

r = 6 % = 0.06   ; n = 10 years   ;    C₁₀ = $ 500 ;

Applying the above values in the formula we have

PV = $ 500 / ( 1 + 0.06 ) ¹⁰

= $ 500 / ( 1.06 ) ¹⁰

= $ 500 / 1.790848

= $ 279.197388

= $ 279.20 ( When rounded off to two decimal places )

Thus the Present value of investment of $ 500 made in 10 years at 6 percent = $ 279.20

Note : The value of ( 1.06 ) ¹⁰ has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.06,10) = 1.790848