Question

Investment X offers to pay you $6,200 per year for nine years, whereas Investment Y offers to pay you $9,000 per year for five years. a. Calculate the present value for Investments X and Y if the discount rate is 4 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b. Calculate the present value for Investments X and Y if the discount rate is 14 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

a)Present value [X] = $46,099.06

    Present value[Y] = $40,066.40

b) Present value[X] = $30,667.51

   Present value[Y] = $30,897.73

Explanation:

Present value of an ordinary annuity is calculated as follows:

$Present value =PMT*\frac{[1-(1+i)^-^n]}{i}$

where PMT = the value of the individual payments in each period

                 i =  the interest rate that would be compounded in each compounding period

                n = the number of payment periods

a) Present value of X given PMT = 6,200; i=0.04; n = 9 is calculated as follows:

Present value[X] = $6,200*\frac{[1-(1+0.04)^-^9]}{0.04}$  = $46,099.06

Present value of Y given PMT = 9,000; i=0.04; n = 5 is calculated as follows:

Present value[Y] = $9,000*\frac{[1-(1+0.04)^-^5]}{0.04}$  = $40,066.40

b) if the discount rate is 14% and all other variables do not change

Present value[X] = $6,200*\frac{[1-(1+0.14)^-^9]}{0.14}$  = $30,667.51

Present value[Y] = $9,000*\frac{[1-(1+0.14)^-^5]}{0.14}$  = $30,897.73