To solve this problem, we can use the formula for simple interest:

$I = P \times r \times t$

where:

• $I$ is the interest earned,
• $P$ is the principal or the initial amount invested,
• $r$ is the annual interest rate,
• $t$ is the time in years.

We know:

• $I = 1888$ dollars,
• $r = 6.4\% = 0.064$,
• $t = 10$ years.

We need to find $P$.

Step-by-Step Solution

1. Substitute the known values into the formula: $1888 = P \times 0.064 \times 10$

2. Simplify the equation: $1888 = P \times 0.64$

3. Solve for $P$ by dividing both sides by 0.64: $P = \frac{1888}{0.64}$

4. Calculate $P$: $P = 2950$

Answer

Dora initially put $2,950 into the account.

Would you like further details or have any questions about this solution?

Here are five related questions that extend this topic:

1. How would the initial investment change if the interest rate were compounded annually instead of being simple interest?
2. What would be the total amount in the account at the end of 10 years, including the principal and interest?
3. If the interest rate were different, say 5%, how would that affect the initial investment needed to earn $1,888 in interest over 10 years?
4. How would the formula change if Dora invested in an account with quarterly compounding interest?
5. What if Dora wanted to earn $3,000 in interest over 10 years? How much would she need to invest initially at the same interest rate?

Tip: For simple interest, the total interest earned grows linearly with time. The formula is simpler than compound interest, which grows exponentially with time due to interest-on-interest effects.