To calculate the savings plan balance after 2 years with an APR of 9% and monthly payments of $150, we use the formula for the future value of an ordinary annuity:

$FV = P \cdot \frac{(1 + r/n)^{nt} - 1}{r/n}$

Where:

• $P = 150$ (monthly payment)
• $r = 0.09$ (annual percentage rate as a decimal)
• $n = 12$ (number of compounding periods per year, since payments are monthly)
• $t = 2$ (time in years)

Step 1: Substitute the values into the formula

$FV = 150 \cdot \frac{(1 + 0.09/12)^{12 \cdot 2} - 1}{0.09/12}$

Step 2: Simplify the terms

• Monthly interest rate: $\frac{0.09}{12} = 0.0075$
• Total number of payments: $12 \cdot 2 = 24$

$FV = 150 \cdot \frac{(1 + 0.0075)^{24} - 1}{0.0075}$

Step 3: Calculate

1. $1 + 0.0075 = 1.0075$
2. $(1.0075)^{24} \approx 1.196899$
3. $1.196899 - 1 = 0.196899$
4. $\frac{0.196899}{0.0075} \approx 26.2532$
5. $150 \cdot 26.2532 \approx 3937.98$

Final Answer:

The savings plan balance after 2 years is approximately $3937.98.

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Do you want further clarifications or need help with any step?
Here are 5 related questions to expand your understanding:

1. How does the APR influence the final balance in a savings plan?
2. What is the difference between an ordinary annuity and an annuity due?
3. How would the balance change if the APR increased to 12%?
4. What would happen to the balance if payments were made annually instead of monthly?
5. How can this formula be adjusted for irregular payment amounts?

Tip: When solving future value problems, ensure that the interest rate and payment frequency are consistent (e.g., monthly rate for monthly payments).