Use the appropriate formula for an annuity and the given variables to solve for the missing variable. Round to the nearest hundredth or cent.

Payments are made at the beginning of the compounding period.  R = $60, r = 1.5%, m = 1, t = 10 years

The problem involves an **annuity due**, where payments are made at the beginning of the compounding period. The formula for the future value $ A $ of an annuity due is:

\[
A = R \times \frac{(1 + r/m)^{mt} - 1}{r/m} \times (1 + r/m)
\]

Where:
- $ A $ = future value of the annuity
- $ R $ = periodic payment amount ($60)
- $ r $ = annual interest rate as a decimal (1.5% = 0.015)
- $ m $ = number of compounding periods per year (1 in this case)
- $ t $ = time in years (10 years)

Let's break it down step by step.

### Step 1: Convert values
- $ R = 60 $
- $ r = 0.015 $
- $ m = 1 $
- $ t = 10 $

### Step 2: Apply the formula

\[
A = 60 \times \frac{(1 + 0.015/1)^{1 \times 10} - 1}{0.015/1} \times (1 + 0.015/1)
\]

\[
A = 60 \times \frac{(1 + 0.015)^{10} - 1}{0.015} \times (1 + 0.015)
\]

\[
A = 60 \times \frac{(1.015)^{10} - 1}{0.015} \times 1.015
\]

### Step 3: Compute values

\[
(1.015)^{10} = 1.160968
\]

\[
A = 60 \times \frac{1.160968 - 1}{0.015} \times 1.015
\]

\[
A = 60 \times \frac{0.160968}{0.015} \times 1.015
\]

\[
A = 60 \times 10.7312 \times 1.015
\]

\[
A = 60 \times 10.8916
\]

\[
A = 653.50
\]

### Final Answer:
The future value $ A $ of the annuity is approximately **$653.50**.

Would you like more details or have any questions? Here are five related questions to further your understanding:

1. How does increasing the interest rate affect the future value of an annuity due?
2. What is the difference between an ordinary annuity and an annuity due?
3. How would the formula change if payments were made at the end of the compounding period (ordinary annuity)?
4. If the number of compounding periods per year changed to 12 (monthly), how would that affect the result?
5. Can the annuity formula be used to calculate the present value instead of the future value?

**Tip:** In an annuity due, payments grow slightly faster than in an ordinary annuity because each payment compounds for one extra period.

Use the appropriate formula for an annuity and the given variables to solve for the missing variable. Round to the nearest hundredth or cent. Payments are made at the beginning of the compounding period. R = $60, r = 1.5%, m = 1, t = 10 years

Learn how to calculate the future value of an annuity due with $60 payments, 1.5% interest, over 10 years. This step-by-step guide covers essential finance concepts like annuities and compound interest. Suitable for students in Grades 10-12 or early college.

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