 
Use the appropriate formula to find the value of the annuity.

b.b. 

Find the interest.

**Periodic Deposit**

**Rate**

**Time**

​$100100 

at the end of every six months

5.5 %5.5% 

compounded semiannually

1515 

years

To calculate the value of an annuity, we can use the **future value of an ordinary annuity formula** since the periodic deposit is made at the end of each period:

\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $A$ is the future value of the annuity (the value of the annuity after 15 years).
- $P$ is the periodic deposit (in this case, \$100,100).
- $r$ is the periodic interest rate (annual rate divided by the number of compounding periods per year).
- $n$ is the total number of payments (number of periods times the number of years).

### Given values:
- Periodic deposit $P = 100,100$
- Annual interest rate = 5.5% or 0.055
- Compounding is **semiannually**, so the number of periods per year = 2
- Time $t = 15$ years

Now, let's calculate the periodic interest rate ($r$) and the total number of periods ($n$):

\[
r = \frac{5.5\%}{2} = \frac{0.055}{2} = 0.0275
\]

\[
n = 15 \times 2 = 30 \text{ periods}
\]

Substitute the values into the formula:

\[
A = 100,100 \times \frac{(1 + 0.0275)^{30} - 1}{0.0275}
\]

I'll calculate this to find the future value of the annuity.The future value of the annuity after 15 years is approximately **\$4,574,030.29**.

### Would you like more details or have any further questions?

Here are 5 related questions that might interest you:
1. How does the formula change if the interest is compounded monthly instead of semiannually?
2. What happens to the annuity's future value if the interest rate increases to 6%?
3. How would the calculation differ if payments were made at the beginning of each period?
4. Can you calculate the total interest earned over 15 years?
5. What is the present value of this annuity if we were to receive it today?

**Tip**: Understanding how compounding works is key in annuity calculations. The more frequently the interest compounds, the higher the future value will be.

Use the appropriate formula to find the value of the annuity. $100,100 at the end of every six months, 5.5% compounded semiannually, for 15 years.

Learn how to calculate the future value of an annuity with $100,100 periodic deposits, compounded semiannually at a 5.5% interest rate over 15 years. Explore step-by-step calculations using the future value of an ordinary annuity formula.

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