Math Problem Statement
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?
Solution
The given formula for the amount in the account is:
In this formula, represents the annual interest rate. Since it's stated as , the annual interest rate is:
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:
- How does quarterly compounding affect the total amount in the account?
- What would be the amount in the account after 2 years?
- How does the interest rate compare to other common savings accounts?
- What factors should one consider when choosing a savings account?
- 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.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Functions
Formulas
A = P(1 + r/n)^(nt)
Theorems
Compound Interest Theorem
Suitable Grade Level
Grades 9-12
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