Why Choose Us?
0% AI Guarantee
Human-written only.
24/7 Support
Anytime, anywhere.
Plagiarism Free
100% Original.
Expert Tutors
Masters & PhDs.
100% Confidential
Your privacy matters.
On-Time Delivery
Never miss a deadline.
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. 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.
Expert Solution
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.
Archived Solution
You have full access to this solution. To save a copy with all formatting and attachments, use the button below.
For ready-to-submit work, please order a fresh solution below.
