Fifth Fourth National Bank has a savings program which will  guarantee you $17,500 in 9 years if you deposit $135 per month. What APR is the bank offering you on this savings plan?


To find the Annual Percentage Rate (APR) offered by the bank, we can use the future value of an ordinary annuity formula:

\[
FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)
\]

Where:
- $FV$ is the future value, which is $17,500.
- $P$ is the monthly deposit, which is $135.
- $r$ is the monthly interest rate.
- $n$ is the number of deposits (9 years × 12 months = 108 deposits).

### Step 1: Set up the equation
Substitute the known values:

\[
17,500 = 135 \times \left(\frac{(1 + r)^{108} - 1}{r}\right)
\]

We now need to solve for $r$, the monthly interest rate, and then convert it to the APR by multiplying by 12.

### Step 2: Solve for $r$
This equation is not easily solved algebraically, so I'll calculate the monthly interest rate numerically.The APR (Annual Percentage Rate) the bank is offering on this savings plan is approximately 3.98%.

Would you like further details or have any other questions?

Here are some related questions you might find useful:
1. How does the future value formula for an annuity differ from other financial formulas?
2. What is the impact of increasing the monthly deposit on the final amount?
3. How would the calculation change if the compounding frequency was daily instead of monthly?
4. What is the difference between APR and APY (Annual Percentage Yield)?
5. How can I calculate the monthly payments if the APR was given instead of the final amount?

**Tip:** Increasing the frequency of compounding generally leads to higher returns due to compound interest.

Fifth Fourth National Bank has a savings program which will guarantee you $17,500 in 9 years if you deposit $135 per month. What APR is the bank offering you on this savings plan?

Learn how to calculate the APR for a savings program that guarantees $17,500 in 9 years with $135 monthly deposits. This solution uses the future value of annuity formula and compound interest concepts to find the approximate APR of 3.98%. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation