Questions: Assume that all interest is simple interest. A local miniature golf course owner must recarpet his fairways and replace the golf clubs his customers use. A bank will lend the owner the necessary 9000 at 9% interest over 108 months. A savings and loan company will lend the owner 9000 at 10% interest for 96 months. Which loan will be less expensive for the golf owner to assume? The total interest paid for the bank loan is 7. The total interest paid for the savings and loan company is 7. The loan from the bank is (Choose one) expensive than the loan from the savings and loan company. more less

Solution Steps

To determine which loan is less expensive, we need to calculate the total interest paid for each loan. The formula for simple interest is \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years.

1. Calculate the total interest for the bank loan.
2. Calculate the total interest for the savings and loan company loan.
3. Compare the two interest amounts to determine which loan is less expensive.

The total interest \( I \) for the bank loan can be calculated using the formula for simple interest:

\[ I_{\text{bank}} = P \times r_{\text{bank}} \times t_{\text{bank}} \]

Substituting the values:

\[ I_{\text{bank}} = 9000 \times 0.09 \times 9 = 7290 \]

Similarly, we calculate the total interest for the savings and loan company loan:

\[ I_{\text{savings}} = P \times r_{\text{savings}} \times t_{\text{savings}} \]

Substituting the values:

\[ I_{\text{savings}} = 9000 \times 0.10 \times 8 = 7200 \]

Now we compare the total interests calculated:

\[ I_{\text{bank}} = 7290 \quad \text{and} \quad I_{\text{savings}} = 7200 \]

Since \( 7290 > 7200 \), the loan from the bank is more expensive than the loan from the savings and loan company.

Final Answer