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Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: , annual interest: , interest periods: 12 , number of years: 10
After 10 years, the investment compounded periodically will be worth more than the investment compounded annually.
(Round to two decimal places as needed.)

Ask by Marsh Wheeler. in the United States
Jan 23,2025

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After 10 years, the investment compounded monthly is worth $167.90 more than the investment compounded annually.

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Beyond the Answer

Let’s first calculate the future value of the investment compounded annually. The formula for calculating future value (FV) when compounded annually is:
Where:
  • is the principal amount ($2000),
  • is the annual interest rate (9% or 0.09),
  • is the number of years (10).
So for compounding annually, we have:
Now, let’s calculate the future value of the investment compounded periodically. The formula for future value when compounded periodically with times a year is:
In this case, the investment is compounded 12 times a year (monthly), so :
Now, we calculate how much more the investment compounded periodically is worth compared to the investment compounded annually:
Thus, after 10 years, the investment compounded periodically will be worth approximately more than the investment compounded annually.

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