# Question Video: Solving Word Problem Involving Percentages and Compound Interests

Amelia opened a retirement account with 7.25% APR in the year 2000. Her initial deposit was \$13500. How much will the account be worth in 2025 if the interest compounded monthly? How much more would she make if the interest compounded continuously?

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### Video Transcript

Amelia opened a retirement account with 7.25 percent APR in the Year 2000. Her initial deposit was 13500 dollars. How much will the account be worth in 2025 if the interest compounded monthly? How much more would she make if the interest compounded continuously?

Using this first formula, π will be the initial amount, π will be the interest rate, π will be the number of times compounded yearly, and π‘ will be the time in years. Plugging this in 13500 per the initial amount, the interest rate of 7.25 percent; written as a decimal, itβs 0.0725. If itβs compounded monthly, thereβs 12 months in a year, so that would be 12. And the number of years that would have went by would be 25 years. So if it were compounded monthly, it would be worth 82247 and 78 cents.

We would use this formula for the interest being compounded continuously, where π is the initial amount, π the interest rate, and π‘ the time in years. Therefore, again 13500 is the initial amount, 0.0725 would be the interest rate written as a decimal, and the years that went by would be 25. So if it compounded continuously, it would be worth 82697 dollars and 53 cents.

Therefore, to answer the question, if it were compounded monthly it will be worth 82247 dollars and 78 cents. If it were compounded continuously, it would be worth 449 dollars and 75 cents more than it was when it was compounded monthly.

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