Question

14.a You bought an annuity that pays $1,000 at the (a) end and (b) beginning of each year next 5 years. If you can earn 6% on your money in other investments with equal risk, the future value (FV) of this kind of annuity is (a) $(                      ) or (b) $(                       _).

14.b You bought an annuity that pays $1,000 at the (a) end or (b) beginning of each year for 5 years. If you can earn 6% on your money in other investments with equal risk, the most you would pay (PV) for this kind of annuity is (a) $(                ) or (b) $(                ).

(Please solve on paper and hand write. No Excel no typed explanation please show all steps)

Answer 1

14.a

a

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

FV= 1000*(((1+ 6/100)^5-1)/(6/100))

FV = 5637.09

b

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

C = Cash flow per period

i = interest rate

n = number of payments

FV= 1000*(((1+ 6/100)^5-1)/(6/100))*(1+6/100)

FV = 5975.32

14.b

a

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

C = Cash flow per period

i = interest rate

n = number of payments

PV= 1000*((1-(1+ 6/100)^-5)/(6/100))

PV = 4212.36

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

C = Cash flow per period

i = interest rate

n = number of payments

PV= 1000*((1-(1+ 6/100)^-5)/(6/100))*(1+6/100)

PV = 4465.11