Question

solve each problem.
1 jenna borrows $8,000 for college at a yearly simple interest rate of 6%. she takes 15 years to pay off the loan and interest. how much interest does she pay? what is the total amount she pays for the loan and interest?
2 mike saves $2,000 at a yearly simple interest rate of 2%. how many years does it take to earn $280 in interest?
3 elliot borrows $900 at a yearly simple interest rate to buy an appliance. he takes 3 years to pay off the loan and interest. he pays $135 in interest. what is the interest rate?
4 robin deposits $500 in a savings account that earns yearly simple interest at a rate of 4%. what is the total amount of money she has after 20 years?

Explanation:

Problem 1: Jenna's Loan

Step 1: Calculate Interest

The formula for simple interest is \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years.
Given \( P = \$8,000 \), \( r = 6\% = 0.06 \), \( t = 15 \) years.
\( I = 8000 \times 0.06 \times 15 \)
\( I = 8000 \times 0.9 \)
\( I = \$7,200 \)

Step 2: Calculate Total Amount

Total amount \( A = P + I \)
\( A = 8000 + 7200 \)
\( A = \$15,200 \)

Step 1: Rearrange Simple Interest Formula for Time

From \( I = P \times r \times t \), solve for \( t \): \( t = \frac{I}{P \times r} \)

Step 2: Substitute Values

Given \( I = \$280 \), \( P = \$2,000 \), \( r = 2\% = 0.02 \).
\( t = \frac{280}{2000 \times 0.02} \)
\( t = \frac{280}{40} \)
\( t = 7 \) years

Step 1: Rearrange Simple Interest Formula for Rate

From \( I = P \times r \times t \), solve for \( r \): \( r = \frac{I}{P \times t} \)

Step 2: Substitute Values

Given \( I = \$135 \), \( P = \$900 \), \( t = 3 \) years.
\( r = \frac{135}{900 \times 3} \)
\( r = \frac{135}{2700} \)
\( r = 0.05 \) or \( 5\% \)

Answer:

Interest: \(\$7,200\); Total Amount: \(\$15,200\)

Problem 2: Mike's Savings