Respuesta :
Answer:
(a) PV = $209.28
(b) PV = $208.33
(c) PV = $207.58
Explanation:
DF = (1 + (i/n) )-n*t
(a) PV= $325 ( 1+(0.09/2) )^-5(2)
PV= $325 x 0.644
PV= $209.28
(b) PV= $325 ( 1+(0.09/4) )^-5(4)
PV =$325 x 0.641
PV =$208.33
(c) PV= $325 (1+(0.09/12) )^-5(12)
PV= $325 x 0.639
PV=$207.58
Answer:
a. $209.28
b. $134.76
c. $191.64
Explanation:
The present value with compound interest equation is the following.
PV = [tex]\frac{A}{(1 + r/n)^nt}[/tex]
Where,
A = Final amount.
PV = Present value
r = interest rate in decimal.
n = number of times the interest is compounded every year.
t = number of years of investment
a. PV = [tex]\frac{A}{(1 + r/n)^nt}[/tex]
A = 325
r = 9% = 0.09
n = 2
t = 5
PV = 325/(1+0.09/2)^2x5
= 325/(1+0.045)^10
= 325/(1.045)^10
= 325/1.552969422
= 209.2764966
= $209.28
That is, the present value of $325 at 9% nominal rate, semiannual compounding, discounted back 5 year is $209.28
b. PV = [tex]\frac{A}{(1 + r/n)^nt}[/tex]
A = 325
r = 9% = 0.09
n = 4
t = 5
PV = 325/(1+0.09/2)^4x5
= 325/(1+0.045)^20
= 325/(1.045)^20
= 325/2.411714025
= 134.7589294
= $134.76
That is, the present value of $325 at 9% nominal rate, quarterly compounding, discounted back 5 year is $134.76
c. PV = [tex]\frac{A}{(1 + r/n)^nt}[/tex]
A = 325
r = 9% = 0.09
n = 12
t = 1
PV = 325/(1+0.09/2)^12x1
= 325/(1+0.045)^12
= 325/(1.045)^12
= 325/1.695881433
= 191.6407561
= $191.64
That is, the present value of $325 at 9% nominal rate, monthly compounding, discounted back 1 year is $191.64
