Elizabeth decides to put 10,000 dollars in a savings account with an interest rate of three percent per year. What is the total amount of money 𝐴 that Elizabeth will have in her savings account after 𝑡 years?
In order to answer this question, we will need to use our compound interest formula. This states that 𝑉 is equal to 𝑃 multiplied by one plus 𝑟 over 100 all raised to the power of 𝑦. 𝑉 is a new value, in this question, the amount of money in Elizabeth’s account. 𝑃 is the principal value or initial value. 𝑟 is the rate of interest as a percentage. And 𝑦 is the number of years. The value inside the parentheses, one plus 𝑟 over 100, is also known as the multiplier.
In this question, we are trying to find the total amount of money 𝐴. We are told the initial investment or principal value is 10,000 dollars. The interest rate is three percent, so we need to multiply 10,000 by one plus three over 100. We’re interested in the amount of money after 𝑡 years. 𝐴 is therefore equal to 10,000 multiplied by one plus three over 100 all raised to the power of 𝑡. Three one hundredths written as a decimal is equal to 0.03. This means that the amount of money 𝐴 is equal to 10,000 multiplied by one plus 0.03 all raised to the power of 𝑡.
This could be simplified one stage further as one plus 0.03 is 1.03. This is our multiplier, and 𝐴 is equal to 10,000 multiplied by 1.03 to the power of 𝑡.