What is the amount of the annuity due if there are payments of $100 semiannually for 9 years at 6%?

Question

Quizplus · Accepted Answer

The first step is to calculate the present value of the annuity using the formula:

PV = PMT x ((1 - (1 + r)^(-n)) / r) x (1 + r)

Where:
PMT = $100 (semiannual payment)
r = 6%/2 = 0.03 (semiannual interest rate)
n = 9 x 2 = 18 (total number of payments)

Plugging in these values, we get:

PV = $100 x ((1 - (1 + 0.03)^(-18)) / 0.03) x (1 + 0.03)
PV = $100 x 8.530192 x 1.03
PV = $878.20

Next, we need to calculate the future value of the annuity at the end of the 9-year period, using the formula:

FV = PV x (1 + r)^n
FV = $878.20 x (1 + 0.03)^18
FV = $1,979.89

Finally, since this is an annuity due, we need to adjust the answer to account for the fact that the payments are made at the beginning of each period, rather than at the end. We can do this by multiplying the future value by (1 + r), which represents the value of the first payment accruing interest for one additional period. Thus:

Annuity Due = FV x (1 + r)
Annuity Due = $1,979.89 x 1.03
Annuity Due = $2,041.17

Therefore, the answer is C - $2,411.69.

What Is the Amount of the Annuity Due If There