Question #135787

Marian Kirk wishes to select the better of two 10-year annuities, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years.

a. Find the future value of both annuities at the end of year 10, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.

b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates.

c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.

d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 10% and (2) 20% interest rates.

e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d.

a. Find the future value of both annuities at the end of year 10, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.

b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates.

c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.

d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 10% and (2) 20% interest rates.

e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d.

Expert's answer

**solution**

Annuity C:

ordinary annuity

Annuity D:

Annuity due

**part a) future value**

**i) when interest **

Annuity C

*answer: the future value is $39,843.56*

Annuity D

*answer: the future value is $32,074.85*

*ii) when interest *

Annuity C

*answer: the future value is $64896.71*

Annuity D

*answer: the future value is $47,957.58*

**part b) **

*answer: the ordinary annuity has a greater present value than the annuity due under both interest rates*

**part c) present value**

**i) when interest **

Annuity C

*answer: the present value is $15,361.42*

Annuity D

*answer: the present value is$14,869.85*

**ii) when interest**

Annuity C

*answer: the present value is$10,481.18*

Annuity D

*answer: the present value is $11,068.13*

**part d)**

*Answer: the present value of the annuity due is greater than that of the ordinary annuity when interest rate is 20%. However, when interest rate is 10%, the present value of the ordinary annuity is greater than that of the annuity due.*

**part e) the present value of the annuities decreased when the interest rate was increased for both annuities. This is because the cash flows are discounted at a higher rate.**

**For both annuities, the future value increased when the interest rate increased from 10% to 20%. This is because cash flows earn higher interest on 20%**

*At 20%, annuity D has a greater present value than annuity C. However, at 10%, annuity C has a greater present value than annuity D*

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