Kenny was given a bonus at work and decided to put it in an interest earning savings account. The quarterly compounded interest and the amount, A, in the account after t years is modeled below.

A=1775(1+ 
12
0.09
​	
 ) 
12t
 

What is the yearly interest rate on this account?

The given formula for the amount \( A \) in the account is:

\[
A = 1775 \left(1 + \frac{0.09}{12}\right)^{12t}
\]

In this formula, \( 0.09 \) represents the annual interest rate. Since it's stated as \( 0.09 \), the annual interest rate is:

\[
0.09 \times 100 = 9\%
\]

Thus, the yearly interest rate on this account is **9%**.

Would you like more details on how this formula works, or do you have other questions? Here are some follow-up questions you might consider:

1. How does quarterly compounding affect the total amount in the account?
2. What would be the amount in the account after 2 years?
3. How does the interest rate compare to other common savings accounts?
4. What factors should one consider when choosing a savings account?
5. How would the total amount change if the interest rate were higher? 

Tip: Always compare the effective annual rate (EAR) when considering different compounding periods.

What is the yearly interest rate on this account?

Discover how to calculate the yearly interest rate for an account with quarterly compounded interest. In this case, the annual interest rate is found to be 9% based on the formula A = 1775(1 + 0.09/12)^(12t). Ideal for high school students studying finance and exponential growth.

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