Question

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $700 per year for 16 years at 8%.

   $  

2. $350 per year for 8 years at 4%.

   $  

3. $200 per year for 8 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $700 per year for 16 years at 8%: $  

   Present value of $350 per year for 8 years at 4%: $  

   Present value of $200 per year for 8 years at 0%: $  

Answer 1

a

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 700*((1-(1+ 8/100)^-16)/(8/100))

PV = 6195.96

b

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 350*((1-(1+ 4/100)^-8)/(4/100))

PV = 2356.46

c

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 200*((1-(1+ 0/100)^-8)/(0/100))

=0

d

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 700*((1-(1+ 8/100)^-16)/(8/100))*(1+8/100)

PV = 6691.64

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 350*((1-(1+ 4/100)^-8)/(4/100))*(1+4/100)

PV = 2450.72

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 200*((1-(1+ 0/100)^-8)/(0/100))*(1+0/100)

=0