Becca deposites $100 into a bank account that earns an annual interest rate of 4% . If she does not make any additional deposits and makes no withdrawals how long will it take her, in year, to increase the value of her account by at least 60%?

Options

A. `12`
B. `15`
C. `25`
D. `30`

Answer

To solve the problem, we need to determine how long it will take for Becca's bank account to increase by at least 60% with an annual interest rate of 4%.

### Step-by-Step Solution:

1. **Identify the Principal Amount (P)**:
Becca deposits $100 into the bank account.
\[ P = 100 \]

2. **Calculate the Target Amount (A)**:
To find out how much she wants to have in her account after increasing it by 60%, we calculate:
\[ \text{Increase} = 60\% \text{ of } 100 = \frac{60}{100} \times 100 = 60 \]
Therefore, the target amount:
\[ A = P + \text{Increase} = 100 + 60 = 160 \]

3. **Use the Simple Interest Formula**:
The formula for simple interest is:
\[ I = \frac{P \times r \times t}{100} \]
where:
- \( I \) is the interest earned,
- \( P \) is the principal amount,
- \( r \) is the annual interest rate,
- \( t \) is the time in years.

4. **Express Total Amount (A) in Terms of Interest**:
The total amount after earning interest can be expressed as:
\[ A = P + I \]
Substituting the interest formula into this equation gives:
\[ A = P + \frac{P \times r \times t}{100} \]

5. **Substitute Known Values**:
We know \( A = 160 \), \( P = 100 \), and \( r = 4\% \):
\[ 160 = 100 + \frac{100 \times 4 \times t}{100} \]

6. **Simplify the Equation**:
The equation simplifies to:
\[ 160 = 100 + 4t \]
Subtract 100 from both sides:
\[ 60 = 4t \]

7. **Solve for Time (t)**:
Divide both sides by 4:
\[ t = \frac{60}{4} = 15 \]

8. **Conclusion**:
It will take Becca 15 years to increase the value of her account by at least 60%.

### Final Answer:
\[ \text{It will take } 15 \text{ years.} \]