QuestionJuly 20, 2025

Find the savings plan balance after 4 years with an APR of 3% and monthly payments of 100 The balance is square (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 3% and monthly payments of 100 The balance is square (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 3%  and monthly payments of 100
The balance is square 
(Do not round until the final answer. Then round to the nearest cent as needed.)

Solution
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Answer

The balance is \5116.63. Explanation 1. Identify the formula Use the future value of an annuity formula: **FV = P \times \frac{(1 + r)^n - 1}{r}**, where P is the monthly payment, r is the monthly interest rate, and n is the total number of payments. 2. Calculate monthly interest rate APR is 3\%, so monthly interest rate r = \frac{0.03}{12} = 0.0025. 3. Determine total number of payments For 4 years with monthly payments, n = 4 \times 12 = 48. 4. Compute future value Substitute P = 100, r = 0.0025, and n = 48 into the formula: FV = 100 \times \frac{(1 + 0.0025)^{48} - 1}{0.0025}. 5. Calculate the result FV = 100 \times \frac{(1.0025)^{48} - 1}{0.0025} \approx 5116.63.

Explanation

1. Identify the formula<br /> Use the future value of an annuity formula: **$FV = P \times \frac{(1 + r)^n - 1}{r}$**, where $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments.<br /><br />2. Calculate monthly interest rate<br /> APR is $3\%$, so monthly interest rate $r = \frac{0.03}{12} = 0.0025$.<br /><br />3. Determine total number of payments<br /> For 4 years with monthly payments, $n = 4 \times 12 = 48$.<br /><br />4. Compute future value<br /> Substitute $P = 100$, $r = 0.0025$, and $n = 48$ into the formula: <br /> $FV = 100 \times \frac{(1 + 0.0025)^{48} - 1}{0.0025}$.<br /><br />5. Calculate the result<br /> $FV = 100 \times \frac{(1.0025)^{48} - 1}{0.0025} \approx 5116.63$.
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