Question

The present value of an annuity due is equal to the present value of an ordinary annuity times (1 + i).

Select one:

True

False

Answer 1

So the statement is correct.

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Let’s se through an example.

PV of annuity due

Present Value of an annuity due is used to determine the present value of a stream of equal payments where the payment occurs at the beginning of each period.

If,

Periodic payment (P) = 100

Interest rate (i) = 0.1

Time period (n) = 2

Then PV of annuity due = P * (1 + i) [1 - {(1+ i)^-n}/i]

Lets put all the values in the formula to find PV of annuity due,

PV of annuity due = 100* (1 + 0.1) [{1- (1 + 0.1)^- 2}/ 0.1]

                                      = 100* (1.1) [{1- (1.1)^- 2}/ 0.1]

                                      = 110[{1- 0.826446281}/ 0.1]

                                      = 110[0.173553719/ 0.1]

                                      = 110* 1.73554

                                      = 190.9094

So PV of annuity due is $190.91

Now we will calculate PV of annuity

              Periodic deposit (P) = $100

              Interest rate = 10%

              Time (n) = 2

Let's put all the values in the formula to find PV o annuity

= 100* [1- (1+ 0.1)^-2]/ 0.1

= 100* [1- (1.1)^-2]/ 0.1

= 100* [1- 0.826446281]/ 0.1

= 100* [0.173553719/ 0.1]

= 100* [1.73553719]

= 173.55

So PV of the amount after 2 years is $173.55

173.55* (1 + 0.1) = 190.909

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