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:
[tex] Present value =PMT*\frac{[1-(1+i)^-^n]}{i}[/tex]
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] = [tex] 6,200*\frac{[1-(1+0.04)^-^9]}{0.04}[/tex] = $46,099.06
Present value of Y given PMT = 9,000; i=0.04; n = 5 is calculated as follows:
Present value[Y] = [tex] 9,000*\frac{[1-(1+0.04)^-^5]}{0.04}[/tex] = $40,066.40
b) if the discount rate is 14% and all other variables do not change
Present value[X] = [tex] 6,200*\frac{[1-(1+0.14)^-^9]}{0.14}[/tex] = $30,667.51
Present value[Y] = [tex] 9,000*\frac{[1-(1+0.14)^-^5]}{0.14}[/tex] = $30,897.73
