Question

Marian Kirk wishes to select the better of two 9​-year annuities. Annuity 1 is an ordinary annuity of ​$2810 per year for 9 years. Annuity 2 is an annuity due of ​$2600 per year for 9 years.

a. Find the future value of both annuities at the end of year 9​, assuming that Marian can earn​ (1) 8​% annual interest and​ (2) 16​% annual interest.

b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 9 for both the​ (1) 8 % and​ (2) 16​% interest rates..

c. Find the present value of both​ annuities, assuming that Marian can earn ​(1) 8​% annual interest and​ (2) 16​% annual interest.

d. Use your findings in part c to indicate which annuity has the greater present value for both the​ (1) 8​% and​ (2) 16​% interest rates.

e. Briefly​ compare, contrast, and explain any differences between your findings using the 8​% and 16​% interest rates in parts b and d.

Answer 1

a]

1]

Future value is calculated using FV function in Excel :

Annuity 1 :

rate = 8%

nper = 9   

pmt = 2810

pv = 0 (beginning amount is zero)

type = 0 (ordinary annuity)

FV is calculated to be $35,090.04

Annuity 2 :

rate = 8%

nper = 9   

pmt = 2600

pv = 0 (beginning amount is zero)

type = 1 (annuity due)

FV is calculated to be $35,065.06

2]

Future value is calculated using FV function in Excel :

Annuity 2 :

rate = 16%

nper = 9   

pmt = 2810

pv = 0 (beginning amount is zero)

type = 0 (ordinary annuity)

FV is calculated to be $49,227.01

Annuity 2 :

rate = 16%

nper = 9   

pmt = 2600

pv = 0 (beginning amount is zero)

type = 1 (annuity due)

FV is calculated to be $52,835.82

b]

With 8% rate, Annuity 1 has higher future value

With 16% rate, Annuity 2 has higher future value

c]

1]

Present value is calculated using PV function in Excel :

Annuity 1 :

rate = 8%

nper = 9   

pmt = 2810

pv = 0 (beginning amount is zero)

type = 0 (ordinary annuity)

PV is calculated to be $17,553.76

Annuity 2 :

rate = 8%

nper = 9   

pmt = 2600

pv = 0 (beginning amount is zero)

type = 1 (annuity due)

PV is calculated to be $17,541.26

2]

Present value is calculated using PV function in Excel :

Annuity 2 :

rate = 16%

nper = 9   

pmt = 2810

pv = 0 (beginning amount is zero)

type = 0 (ordinary annuity)

PV is calculated to be $12,944.39

Annuity 2 :

rate = 16%

nper = 9   

pmt = 2600

pv = 0 (beginning amount is zero)

type = 1 (annuity due)

PV is calculated to be $13,893.34

d]

With 8% rate, Annuity 1 has higher present value

With 16% rate, Annuity 2 has higher present value