Sam opened a money-market account that pays 5% simple interest. He started the account with $7,000 and made no further deposits. When he closed the account, he had earned $1,750 in interest. How long did he keep his account open?

Question

A.
7 years
B.
5 years
C.
6 years
D.
8 years

Answer 1

To find out how long Sam kept his money-market account open, we 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.

From the problem, we have:

• \( I = 1,750 \)
• \( P = 7,000 \)
• \( r = 5% = 0.05 \)

We need to solve for \( t \):

\[ 1,750 = 7,000 \times 0.05 \times t \]

First, calculate \( 7,000 \times 0.05 \):

\[ 7,000 \times 0.05 = 350 \]

Now, we can substitute this back into our equation:

\[ 1,750 = 350 \times t \]

To find \( t \), divide both sides by 350:

\[ t = \frac{1,750}{350} = 5 \]

So, Sam kept his account open for 5 years. Therefore, the correct answer is:

B. 5 years