Sasha invested $1,200 in a savings account at an annual interest rate of 1.6% compounded annually. She made no further deposits or withdrawals. To the nearest dollar, how much more money did she have in the account after 3 years than after 2 years?

Answer

To solve the problem, we will use the formula for compound interest to find the amount in the savings account after 2 years and after 3 years, and then we will calculate the difference between these two amounts.

### Step-by-Step Solution:

1. **Identify the variables:**
- Principal amount (P) = $1,200
- Annual interest rate (r) = 1.6% = 0.016 (as a decimal)
- Time (t) for the first calculation = 2 years
- Time (t) for the second calculation = 3 years

2. **Use the compound interest formula:**
The formula for the amount A after t years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]

3. **Calculate the amount after 2 years (A2):**
\[ A_2 = 1200 \left(1 + \frac{1.6}{100}\right)^2 \]
\[ A_2 = 1200 \left(1 + 0.016\right)^2 \]
\[ A_2 = 1200 \left(1.016\right)^2 \]
\[ A_2 = 1200 \times 1.032256 \]
\[ A_2 \approx 1238.71 \text{ (rounding to the nearest dollar gives } 1239) \]

4. **Calculate the amount after 3 years (A3):**
\[ A_3 = 1200 \left(1 + \frac{1.6}{100}\right)^3 \]
\[ A_3 = 1200 \left(1 + 0.016\right)^3 \]
\[ A_3 = 1200 \left(1.016\right)^3 \]
\[ A_3 = 1200 \times 1.048576 \]
\[ A_3 \approx 1258.29 \text{ (rounding to the nearest dollar gives } 1259) \]

5. **Find the difference between the amounts after 3 years and 2 years:**
\[ \text{Difference} = A_3 - A_2 \]
\[ \text{Difference} = 1259 - 1239 \]
\[ \text{Difference} = 20 \]

### Final Answer:
Sasha has $20 more in the account after 3 years than after 2 years.

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