Questions: Find the savings plan balance after 4 years with an APR of 8% and monthly payments of 250. The balance is ... (Do not round until the final answer. Then round to the nearest cent as needed.)

Find the savings plan balance after 4 years with an APR of 8% and monthly payments of 250. The balance is ... (Do not round until the final answer. Then round to the nearest cent as needed.)
Transcript text: Find the savings plan balance after 4 years with an APR of $8 \%$ and monthly payments of $\$ 250$. 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 interest rate from a percentage to a decimal

Given an APR of 8%, we convert this to a decimal: \(r_d = \frac{8}{100} = 0.08\).

Step 2: Calculate the monthly interest rate

The monthly interest rate is calculated by dividing the annual rate by 12: \(r_m = \frac{r_d}{12} = 0.00667\).

Step 3: Calculate the total number of payments

The total number of payments over 4 years is: \(t = n \times 12 = 48\).

Step 4: Use the future value of a series formula to calculate the balance

Using the future value of a series formula: \(FV = P \times \left( \frac{(1 + r_m)^t - 1}{r_m} \right) = 14087.48\).

Final Answer:

The balance of the savings plan after 4 years with an APR of 8% and monthly payments of 250 is approximately $14087.48.

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