Work each problem. Levada borrows \$30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%. How much must she pay the bank in 18 months?

Verified step by step guidance

1. Identify the principal amount (P), the annual interest rate (r), and the time period (t) in years. Here, P = 30900, r = 5.5% (or 0.055 as a decimal), and t = 18 months, which needs to be converted to years by dividing by 12.
2. Convert the time period from months to years: \(t = \frac{18}{12}\) years.
3. Use the simple interest formula to calculate the interest: \(I = P \times r \times t\).
4. Calculate the interest amount by substituting the values of P, r, and t into the formula.
5. Add the interest to the principal to find the total amount to be repaid: \(A = P + I\).

Key Concepts

Simple Interest Formula

Simple interest is calculated using the formula I = PRT, where I is the interest, P is the principal amount, R is the annual interest rate (in decimal), and T is the time in years. This formula helps determine the total interest accrued over a specific period.

Converting Time to Years

Since interest rates are typically annual, the time period must be expressed in years. For example, 18 months is converted to 1.5 years by dividing the number of months by 12. This ensures accurate calculation of interest.

Total Amount to be Repaid

The total amount to be repaid is the sum of the principal and the interest. After calculating the interest using the simple interest formula, add it to the original loan amount to find the total repayment required.