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Q- Suppose you are going to receive Rs

Finance

Q- Suppose you are going to receive Rs. 83,800 per year for five years. The appropriate interest rate is 7.3 percent.

 

a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due?

 

b. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are an annuity due?

Which has the highest present value, the ordinary annuity or annuity due? Which has the highest future value? Will this always be true?

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1) Computation of Present Value of Ordinary Annuity and Present Value of Annuity Due:

Present Value of Ordinary Annuity = PMT*((1-(1+r)^-n)/r) 

=83800*((1-(1+7.3%)^-5)/7.3%) 

= $340,854.12


Present Value of Annuity Due =(1+r)*PMT*((1-(1+r)^-n)/r) 

=(1+7.3%)*83800*((1-(1+7.3%)^-5)/7.3%) 

= $365,736.47
 

2) Computation of Future Value of Ordinary Annuity and Future Value of Annuity Due:
Future Value of Ordinary Annuity = PMT*((1+r)^n-1)/r) 

=83800*((1+7.3%)^5-1)/7.3%) 

= $484,805.08
 

Future Value of Annuity Due =(1+r)*PMT*((1+r)^n-1)/r) 

=(1+7.3%)*83800*((1+7.3%)^5-1)/7.3%) 

= 520195.85

 

PV of annuity due and FV of annuity due value is highest. This is because when rate is greater than 0% than annuity is always greater than ordinary annuity. At rate of 0% ordinary annuity and annuity due value will be same.

 

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