Question

1. michael opened a bank account. he put some money into it. he earned 3% simple interest per year. he earned a total of $120 in interest over five years. how much money did he put into his account when he opened it?

120 ÷ 5 = 24
24 - 0.72 =23.28
24 × 0.03 =0.72

Explanation:

Step1: Recall simple interest formula

The simple interest formula is \( I = P \times r \times t \), where \( I \) is the interest, \( P \) is the principal (initial amount), \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years. We know \( I = 120 \), \( r = 3\%= 0.03 \), and \( t = 5 \) years. We need to solve for \( P \). Rearranging the formula for \( P \), we get \( P=\frac{I}{r\times t} \).

Step2: Substitute the known values

Substitute \( I = 120 \), \( r = 0.03 \), and \( t = 5 \) into the formula: \( P=\frac{120}{0.03\times5} \).

Step3: Calculate the denominator first

Calculate \( 0.03\times5 = 0.15 \).

Step4: Calculate the principal

Now, \( P=\frac{120}{0.15}= 800 \). Wait, but looking at the handwritten notes, there seems to be a miscalculation. Wait, let's re - check the problem. Wait, the handwritten note has \( 120\div5 = 24 \), then \( 24\div0.03=800 \)? Wait, no, the handwritten note has \( 24\times0.03 = 0.72 \), which is wrong. Let's do it correctly.

Correct steps:

Step1: Recall the simple interest formula

\( I = P\times r\times t \), so \( P=\frac{I}{r\times t} \)

Step2: Convert the rate to decimal

\( r = 3\%=0.03 \), \( t = 5 \) years, \( I = 120 \)

Step3: Substitute values into the formula for \( P \)

\( P=\frac{120}{0.03\times5} \)

Step4: Calculate the denominator

\( 0.03\times5=0.15 \)

Step5: Calculate \( P \)

\( P = \frac{120}{0.15}=800 \)

But the handwritten work has an error. Let's check the handwritten steps: The first handwritten step is \( 120\div5 = 24 \) (this is \( I\div t \), which would be the annual interest, since \( I = P\times r\times t\), so annual interest \( I_{annual}=P\times r\)). Then if \( I_{annual}=24 \) (from \( 120\div5 \)), and \( r = 0.03 \), then \( P=\frac{I_{annual}}{r}=\frac{24}{0.03}=800 \). Ah, that's another way. So:

Step1: Find the annual interest

Since the total interest over 5 years is 120, the annual interest \( I_{annual}=\frac{120}{5}=24 \)

Step2: Use the annual interest formula \( I_{annual}=P\times r \)

We know \( I_{annual} = 24 \) and \( r=0.03 \), so \( P=\frac{I_{annual}}{r}=\frac{24}{0.03} \)

Step3: Calculate \( P \)

\( \frac{24}{0.03}=800 \)

Answer:

The amount of money Michael put into the account (the principal) is \(\$800\)