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Homework answers / question archive / Ordinary annuity versus annuity due Marian Kirk wishes to select the better of two 10-year annuities, C and D

Ordinary annuity versus annuity due Marian Kirk wishes to select the better of two 10-year annuities, C and D

Finance

Ordinary annuity versus annuity due 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.

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a-1). Computation of the future value of annuity C at 10% interest rate:-

FV of annuity C = Annuity*(((1+rate)^n-1)/rate)

= $2,500*(((1+10%)^10-1)/10%)

= $2,500*15.9374

= $39,843.56

 

Computation of the future value of annuity D at 10% interest rate:-

FV of annuity D = Annuity*(((1+rate)^n-1)/rate)*(1+rate)

= $2,200*(((1+10%)^10-1)/10%)*(1+10%)

= $2,200*15.9374*1.10

= $38,568.57

 

a-2). Computation of the future value of annuity C at 20% interest rate:-

FV of annuity C = Annuity*(((1+rate)^n-1)/rate)

= $2,500*(((1+20%)^10-1)/20%)

= $2,500*25.9587

= $64,896.71

 

Computation of the future value of annuity D at 20% interest rate:-

FV of annuity D = Annuity*(((1+rate)^n-1)/rate)*(1+rate)

= $2,200*(((1+20%)^10-1)/20%)*(1+20%)

= $2,200*25.9587*1.20

= $68,530.92

b-1). Annuity C has higher future value at 10% interest rate.

b-2). Annuity D has higher future value at 20% interest rate.

c-1). Computation of the present value of annuity C at 10% interest rate:-

PV of annuity C = Annuity*(((1-1/(1+rate)^n)/rate)

= $2,500*(((1-1/(1+10%)^10)/10%)

= $2,500*6.1446

= $15,361.42

 

Computation of the present value of annuity D at 10% interest rate:-

PV of annuity D = Annuity*(((1-1/(1+rate)^n)/rate)*(1+rate)

= $2,200*(((1-1/(1+10%)^10)/10%)*(1+10%)

= $2,200*6.1446*1.10

= $14,869.85

 

c-2). Computation of the present value of annuity C at 20% interest rate:-

PV of annuity C = Annuity*(((1-1/(1+rate)^n)/rate)

= $2,500*(((1-1/(1+20%)^10)/20%)

= $2,500*4.1925

= $10,481.18

 

Computation of the present value of annuity D at 20% interest rate:-

PV of annuity D = Annuity*(((1-1/(1+rate)^n)/rate)*(1+rate)

= $2,200*(((1-1/(1+20%)^10)/20%)*(1+20%)

= $2,200*4.1925*1.20

= $11,068.13

 

d-1). Annuity C has higher present value at 10% interest rate.

d-2). Annuity D has higher present value at 20% interest rate.

e). At 10% interest rate the future value and the present value for annuity C is higher than annuity D. So, the annuity C is better at 10% interest rate than annuity D.

At 20% interest rate the future value and the present value for annuity D is higher than annuity C. So, the annuity D is better at 20% interest rate than annuity C.

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