Questions: Question 4, 4.C. 17 HW Score: 16.67%, 3 of 18 points Points: 0 of 1 Find the savings plan balance after 4 years with an APR of 5% and monthly payments of 150. The balance is (Do not round until the final answer. Then round to the nearest cent as needed.)

Question 4, 4.C. 17 HW Score: 16.67%, 3 of 18 points Points: 0 of 1 Find the savings plan balance after 4 years with an APR of 5% and monthly payments of 150. The balance is (Do not round until the final answer. Then round to the nearest cent as needed.)
Transcript text: Question 4, 4.C. 17 HW Score: 16.67\%, 3 of 18 points Points: 0 of 1 Find the savings plan balance after 4 years with an APR of $5 \%$ and monthly payments of $\$ 150$. The balance is $\$$ $\square$ (Do not round until the final answer. Then round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Convert the Annual Percentage Rate (APR) to a monthly interest rate

To find the monthly interest rate, divide the APR by 12 and convert it to a decimal. For an APR of 5%, the monthly interest rate \(i\) is \(\frac{5}100 \div 12 = 0.00417\).

Step 2: Apply the future value of an annuity formula

The formula for the future value \(FV\) of a series of equal payments \(P\) made at the end of each period, compounded at a periodic interest rate \(i\), over \(n\) periods is: \[ FV = P \times \left( \frac{{(1 + i)^n - 1}}{{i}} \right) \] Substituting the values, we get \( FV = 150 \times \left( \frac{(1 + 0.00417)^48 - 1}{0.00417} \right) \).

Step 3: Calculate the future value

Using the formula, the future value of the savings plan after 48 periods is calculated to be 7952.23.

Final Answer:

The balance of the savings plan after 48 periods, with an APR of 5% and monthly payments of 150, rounded to 2 decimal places, is 7952.23.

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