The amount of annuity due consisting 15 annual payments invested at 8?
**The Amount of Annuity Due consisting of 15 Annual Payments invested at 8%**
An annuity is a series of equal payments made at regular intervals over a specified period of time. In the case of an annuity due, the payments are made at the beginning of each period. In this question, we are given that the annuity consists of 15 annual payments and is invested at a rate of 8%.
To calculate the amount of the annuity due, we can use the formula for the future value of an annuity due:
FV = P * [(1 + r) * ((1 + r)^n - 1) / r]
Where:
FV = Future Value of the annuity
P = Payment amount
r = Rate of interest per period
n = Number of periods
**Step 1: Calculate the Future Value of the Annuity Due**
In this case, we need to calculate the future value of the annuity due. The payment amount (P) is not given in the question, so let's assume it to be X.
FV = X * [(1 + 0.08) * ((1 + 0.08)^15 - 1) / 0.08]
Simplifying the equation,
FV = X * [1.08 * (1.08^15 - 1) / 0.08]
**Step 2: Solve for X**
To determine the value of X, we need to solve the equation above. We can do this by dividing both sides of the equation by the expression inside the square brackets:
FV / [1.08 * (1.08^15 - 1) / 0.08] = X
**Step 3: Calculate the Value of X**
Now, let's substitute the given values into the equation to find the value of X:
FV = X * [1.08 * (1.08^15 - 1) / 0.08]
Substituting the values,
FV = X * [1.08 * (1.667 - 1) / 0.08]
Simplifying further,
FV = X * [1.08 * 0.667 / 0.08]
FV = X * 8.835
Dividing both sides of the equation by 8.835,
X = FV / 8.835
**Step 4: Calculate the Amount of the Annuity Due**
Now that we have the value of X, we can calculate the amount of the annuity due. Since the annuity consists of 15 annual payments, the total amount of the annuity due will be:
Amount of Annuity Due = X * 15
Substituting the value of X, we get:
Amount of Annuity Due = (FV / 8.835) * 15
Therefore, the amount of the annuity due consisting of 15 annual payments invested at 8% can be calculated using the formula above.