Question Video: Forming Exponential Functions Involving Compound Interest | Nagwa Question Video: Forming Exponential Functions Involving Compound Interest | Nagwa

# Question Video: Forming Exponential Functions Involving Compound Interest Mathematics • Second Year of Secondary School

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Elizabeth decides to put \$10,000 in a savings account with an interest rate of 3% per year. What is the total amount of money π΄ that Elizabeth will have in her savings account after π‘ years?

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### Video Transcript

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 π΄ that Elizabeth will have in her savings account after π‘ years?

In order to answer this question, we will need to use our compound interest formula. This states that π is equal to π multiplied by one plus π over 100 all raised to the power of π¦. π is a new value, in this question, the amount of money in Elizabethβs account. π is the principal value or initial value. π is the rate of interest as a percentage. And π¦ is the number of years. The value inside the parentheses, one plus π over 100, is also known as the multiplier.

In this question, we are trying to find the total amount of money π΄. 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. Weβre interested in the amount of money after π‘ years. π΄ is therefore equal to 10,000 multiplied by one plus three over 100 all raised to the power of π‘. Three one hundredths written as a decimal is equal to 0.03. This means that the amount of money π΄ is equal to 10,000 multiplied by one plus 0.03 all raised to the power of π‘.

This could be simplified one stage further as one plus 0.03 is 1.03. This is our multiplier, and π΄ is equal to 10,000 multiplied by 1.03 to the power of π‘.

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