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To solve this problem, we are dealing with an **ordinary annuity** where payments are made at the end of each year, with a 3% interest rate compounded annually. 

The formula for the future value of an ordinary annuity is:

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

Where:
- $FV$ = future value of the annuity
- $P$ = annual payment (deposit) = \$1100
- $r$ = interest rate per period (annual rate = 3%, so $r = 0.03$)
- $n$ = number of periods (years)

### (a) Find the total value of the annuity at the end of the 1st year.
For the first year:
- $n = 1$
- Plugging into the formula:

\[
FV_1 = 1100 \times \left( \frac{(1 + 0.03)^1 - 1}{0.03} \right)
\]

### (b) Find the total value of the annuity at the end of the 2nd year.
For the second year:
- $n = 2$

\[
FV_2 = 1100 \times \left( \frac{(1 + 0.03)^2 - 1}{0.03} \right)
\]

### (c) Find the total value of the annuity at the end of the 3rd year.
For the third year:
- $n = 3$

\[
FV_3 = 1100 \times \left( \frac{(1 + 0.03)^3 - 1}{0.03} \right)
\]

Now, I will compute these values.The future values of the annuity are as follows:

- (a) At the end of the 1st year: \$1100.00
- (b) At the end of the 2nd year: \$2233.00
- (c) At the end of the 3rd year: \$3399.99

Would you like more details on how these calculations were made or have any further questions?

Here are 5 related questions:
1. How does the formula for an ordinary annuity change if payments are made at the beginning of each year?
2. What would be the total value of the annuity if the interest rate was 5% instead of 3%?
3. How does the future value change if the investor deposits \$1500 instead of \$1100 each year?
4. What is the difference between an ordinary annuity and an annuity due?
5. How would the future value of the annuity differ if it compounded semi-annually?

**Tip:** When solving annuity problems, be sure to check if it is an "ordinary annuity" or an "annuity due," as this changes when the payments are made and affects the future value calculation.

An investor wants to save money to purchase real estate. He deposits $1100 at the end of each year in an ordinary annuity that pays 3% interest, compounded annually. (a) Find the total value of the annuity at the end of the 1st year. (b) Find the total value of the annuity at the end of the 2nd year. (c) Find the total value of the annuity at the end of the 3rd year.

Learn how to calculate the future value of an ordinary annuity where an investor deposits $1100 annually at a 3% interest rate compounded annually. This step-by-step guide covers the calculation for the 1st, 2nd, and 3rd years.

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