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Anthony invests money in an account paying a simple interest of per year. If represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?
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Q. Anthony invests money in an account paying a simple interest of per year. If represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?
- Identify variables and formula: Identify the variables and the formula for simple interest.Simple interest is calculated using the formula , where is the interest earned, is the principal amount (initial investment), is the annual interest rate, and is the time in years. Since we are looking for the balance after a year, we need to add the interest earned to the initial investment.
- Convert interest rate to decimal: Convert the annual interest rate from a percentage to a decimal.The interest rate given is , which as a decimal is (since ).
- Calculate interest earned: Calculate the interest earned after one year.Using the formula for simple interest, we have , where is the initial investment and we multiply by because the time period is one year.
- Calculate total balance: Calculate the total balance after one year.The total balance is the initial investment plus the interest earned, so the balance after one year is . Substituting the expression for from Step , we get .
- Simplify total balance expression: Simplify the expression for the total balance. Simplify the expression to , which can be further simplified to .
- Combine like terms: Combine like terms to get the final expression.Combine and to get . This is the expression that represents Anthony's balance after a year with simple interest of per year.
