Luis Sanchez borrowed 3150 dollars from his brother Julio to...

Luis Sanchez borrowed 3150 dollars from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at $8 \%$.
(a) How much will the interest amount to?
(b) What amount must Luis pay Julio at the end of the 6 months?

Key Concepts

Total Repayment Calculation

The total repayment calculation involves summing the original principal and the interest accrued over the borrowing period. This concept is crucial in financial transactions, as it determines the complete amount that must be repaid at the end of the lending period, providing clarity on the total cost of the loan.

Principal

The principal is the original sum of money that is borrowed or invested before any interest is applied. It is the base amount on which interest is calculated and repaid gradually over time. Understanding the principal is essential for determining the total cost of a loan or the returns on an investment.

Simple Interest

Simple interest is a method of calculating interest that does not compound; the interest is computed solely on the original principal. This means that the interest accumulated over each period remains constant, making it straightforward to predict the total repayment or investment return over time.

Interest Rate

The interest rate is the percentage at which interest accumulates on the principal over a specified time period, usually expressed as an annual percentage. It is a crucial factor in determining how much additional money will be owed or earned, and its application in simple interest calculations ensures proportional growth with respect to time.

Time Period in Interest Calculations

The time period in interest calculations refers to the duration for which the principal amount is subject to interest. For annual interest rates, the time is often expressed in years. When the time period is given in months, it needs to be converted to a fraction of a year (for example, 6 months is 0.5 years) to ensure accurate computation of interest.

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