### 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, itβs
0.0725. If itβs compounded monthly, thereβs
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.