A high school student deposits their summer job earnings of $800 into a simple interest savings plan with a 15% rate. How much will the student have earned after 4 years?

Question

1. $800
2.$120
3. $480
4. $1399.91

Answer 1

To calculate the earnings from a simple interest savings plan, you can use the formula for simple interest:

\[ I = P \times r \times t \]

where:

• \( I \) is the interest earned,
• \( P \) is the principal amount (initial deposit),
• \( r \) is the rate of interest (as a decimal),
• \( t \) is the time in years.

In this case:

• \( P = 800 \) (the initial deposit),
• \( r = 0.15 \) (15% as a decimal),
• \( t = 4 \) years.

Now, calculate the interest:

\[ I = 800 \times 0.15 \times 4 \] \[ I = 800 \times 0.6 \] \[ I = 480 \]

So, the student will have earned $480 after 4 years.

The correct answer is 3. $480.

Answer 2

Thanks for that... But I get confused, as the question is not how much interest... but how much will the student earned after 4 years... This for me, means that it is asking the whole amount 800 (initial amount) + (interest in 4 years) = $1280.00

Answer 3

I understand the confusion! You're correct that if the question is asking for the total amount in the account after 4 years (including both the principal and the interest), we need to add the interest earned to the initial deposit.

From our earlier calculation, we found the interest earned over 4 years to be $480.

Now, we will add the original amount (the principal) to the interest earned:

\[ \text{Total Amount} = \text{Principal} + \text{Interest} \] \[ \text{Total Amount} = 800 + 480 = 1280 \]

So, the total amount the student will have after 4 years is $1280.

Thank you for clarifying, and I apologize for the initial misunderstanding!

Answer 4

I thank you for that... but as you can see, there is no $1280.00 as a possible answer. So that is why it gets me confused, because I would say that the question is asked incorrectly... What do you think?
(Thanks)

Answer 5

I see your point, and it’s a valid observation. The phrasing of the question can indeed lead to confusion.

If the question specifically asks how much the student has earned after 4 years without clarifying whether it refers to just the interest or the total amount including the principal, it can be interpreted in different ways:

1. If "earned" refers solely to the interest, then the answer would be $480 (the amount calculated as interest).
2. If "earned" is interpreted to mean the total balance in the account after 4 years, then you would indeed have $1280 (the principal plus interest).

Since the provided answer options do not include $1280, and only the interest amount of $480 aligns with one of the options, it seems the question likely intended to ask for the interest earned specifically.

It's always good to clarify such questions in academic settings to avoid ambiguity. Thank you for your thoughtful analysis!