After 36 months (3 years), how much money will be in the account?

Steps to Solve

1. Create a Table

To begin, we can calculate the amount in the bank account for the first few months. The amount triples each month.

To calculate subsequent months, use the formula:

$$ \text{Amount}{n} = 3 \times \text{Amount}{n-1} $$

2. Continue Table Calculation

Continue calculating the values for all months up to 36:

• Month 0: $10
• Month 1: $10 × 3 = $30
• Month 2: $30 × 3 = $90
• Month 3: $90 × 3 = $270
• Month 4: $270 × 3 = $810
• Month 5: $810 × 3 = $2430
• Continue until Month 36.

3. Formulate an Equation

The amount in the account can be described with the exponential function:

$$ A(n) = 10 \times 3^n $$

Where $A(n)$ is the amount after $n$ months.

4. Calculate Amount After 36 Months

Now, plugging in $n = 36$ in our equation:

$$ A(36) = 10 \times 3^{36} $$

Calculating this gives the amount after 36 months.

5. Final Calculation

Now we will calculate $3^{36}$ using a calculator:

$$ A(36) = 10 \times 3^{36} \approx 10 \times 7.62559748 \times 10^{16} $$