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 AA in the account is:

A=1775(1+0.0912)12tA = 1775 \left(1 + \frac{0.09}{12}\right)^{12t}

In this formula, 0.090.09 represents the annual interest rate. Since it's stated as 0.090.09, the annual interest rate is:

0.09×100=9%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.

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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