Respuesta :
Answer:
a1) $57,402.76
a2) $61,420.96
b1) $80,510.34
b2) $86,146.07
c1) Annuity Due
c2) Annuity Due
Explanation:
Suppose you are going to receive $14,000 per year for five years. The appropriate interest rate is 7 percent. a-1. What is the present value of the payments if they are in the form of an ordinary annuity?
An ordinary annuity is such that is paid at the end of every year
PV of an Annuity = C x [ (1 – (1+i)-n) / i ]
Where,
C is the cash flow per period = $14,000
i is the rate of interest = 7%
n is the frequency of payments = 5 years
14,000 x [(1-(1+0.7)^-5)/0.7] = $57,402.76
a-2. What is the present value of the payments if the payments are an annuity due?
An annuity due is such that is paid at the start of every period
we will use the same formula but the number of years will be 4, signifying the beginning of the 4 years, and then we will add 14,000 to the answer because that amount will be received now.
PV of an Annuity = C x [ (1 – (1+i)-n) / i ]
Where,
C is the cash flow per period = $14,000
i is the rate of interest = 7%
n is the frequency of payments = 4 years
14,000 x [(1-(1+0.7)^-4)/0.7] = $47,420.96
To this amount we add $14,000 = $61,420.96
b-1. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity?
FV = C× (1+r)^ n −1) /r
where:
C=Dollar amount of each annuity payment
r=Interest rate (also known as discount rate)
n=Number of periods in which payments will be made
FV = 14,000 x ((1+0.07)^5 -1)/0.07 = $80,510.34
b-2. What is the future value if the payments are an annuity due?
FV = C× ( (1+r)^ n ) −1) /r x (1+r)
FV = 14,000 x ((1+0.07)^5 -1)/0.07 x(1.07)= $86,146.07
c-1. Which has the higher present value, the ordinary annuity or annuity due?
Annuity Due
c-2. Which has the higher future value?
Annuity Due
