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%. (a)How much must she pay the bank in 18 months?

Verified step by step guidance

1. Identify the formula for simple interest: $I=P\times r\times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the rate of interest per year, and $t$ is the time in years.
2. Convert the time period from months to years. Since there are 12 months in a year, 18 months is equivalent to $\frac{18}{12}=1.5$ years.
3. Substitute the given values into the simple interest formula: $P=30900$, $r=0.055$, and $t=1.5$.
4. Calculate the interest $I$ using the formula: $I=30900\times 0.055\times 1.5$.
5. Add the interest $I$ to the principal $P$ to find the total amount Levada must pay back: Total Payment = $P+I$.

Key Concepts

Simple Interest Formula

The simple interest formula calculates the interest earned or paid on a principal amount over a specific period. It is expressed as I = PRT, where I is the interest, P is the principal amount, R is the annual interest rate (as a decimal), and T is the time in years. This formula is essential for determining how much interest Levada will owe on her loan.

Principal Amount

The principal amount is the initial sum of money borrowed or invested, before any interest is applied. In this scenario, Levada's principal is $30,900, which is the amount she needs to repay along with the interest accrued over the 18-month period. Understanding the principal is crucial for calculating the total repayment amount.

Time Conversion

Time conversion is necessary when dealing with interest calculations, especially when the time period is not in years. Since the loan term is given in months (18 months), it must be converted to years for the simple interest formula. This is done by dividing the number of months by 12, resulting in 1.5 years for this problem.