Video: Solving Word Problems by Calculating the Interest Rate on an Investment given the Time Period and the Interest

Benjamin deposited $2420 in a savings account, and it earned $363.00 in simple interest after five years. Find the interest rate on Benjaminโ€™s savings account.

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Video Transcript

Benjamin deposited 2420 dollars in a savings account, and it earned 363 dollars in simple interest after five years. Find the interest rate on Benjaminโ€™s savings account.

So first, Benjamin deposited 2420 dollars into his savings account. So it should save money. After five years, he earned 363 dollars in simple interest. So it would be what he deposited plus that amount. And weโ€™re asked to find the interest rate.

There is a simple interest formula that we can use: ๐ผ equals ๐‘ƒ๐‘Ÿ๐‘ก, where ๐ผ is the simple interest earned and we know that that was 363 dollars, ๐‘ƒ stands for the principle amount โ€” the amount that would have been deposited โ€” so 2420, ๐‘Ÿ is the interest rate which we donโ€™t know, and then ๐‘ก is the time, which was five years.

So so letโ€™s begin solving for the interest rate, ๐‘Ÿ. First, letโ€™s get rid of the 2420, so divide both sides of the equation by it. So we have 0.15 is equal to five times ๐‘Ÿ. So to solve for ๐‘Ÿ, we would now divide by five to both sides. And we find that ๐‘Ÿ is equal to 0.03.

Now, ๐‘Ÿ is an interest rate. So it should be written as a percent. And to write it as a percent, we essentially need to multiply this by 100 or thinking of it as moving the decimal point two places to the right, which would give us three, or imagine moving the digits two places to the left.

Either way, we have found that the interest rate for Benjamin savings account will be three percent.

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