Looking for the formula and breakdown for the following question ? How the answe
ID: 2612631 • Letter: L
Question
Looking for the formula and breakdown for the following question ? How the answer was found ?
Calculating Annuities Due- Suppose you are going to recieve $15,800 per year for five years. The appropriate interest rate is 7.9 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 of 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 oridnary annuity ? What if the payments are annuity due ?
(c) Which has the highest present value, the ordinary annuity or annuity due ? which has the highest future value ? Will this always be true ?
Explanation / Answer
A. Present Value of the given Ordinary Annuity= C* [1-(1+i)-n]/ i = 15800 * [1-(1+0.079)-5] / 0.079= $63,254.44
Present Value of Annuity Due= C * {[1-(1+i)-n]/ i} * (1+i)= 15800 * {[1-(1+0.079)-5] / 0.079}* (1 + 0.079)
= $63,254.44 * (1.079)= $68,248.30
B.
Future Value of the given Ordinary Annuity= C* [(1+i)n-1]/ i = 15800 * [(1+0.079)5 - 1] / 0.079= $92,507.64
Future Value of Annuity Due= C* {[(1+i)n-1]/ i} * (1+i) = 15800 * {[(1+0.079)5 - 1] / 0.079} * (1 + 0.079)
= $92,507.64 * (1.079)= $99,815.75
C.
Present Value of Annuity Due will be the highest of the two Present Values
Future Value of Annuity Due will be the highest og the two Future Values
This will always be true because for the present value of an annuity due formula, we need to discount the formula one period forward as the payments are held for a lesser amount of time. When calculating the present value, we assume that the first payment was made today.
For Future Value case, since each payment in the series is made one period sooner, we need to discount the formula one period back i.e. each payment is made at the beginning of the period rather than at the end of the period. A slight modification to the FV-of-an-ordinary-annuity formula accounts for payments occurring at the beginning of each period.
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