QuestionAugust 24, 2025

Ronald deposited 635 at the end of every 6 months in an account that pays 7% , compounded semi- annually. How much money will he have in the account in 4 years? 5,747.82 4,003 2,676.49 3,856

Ronald deposited 635 at the end of every 6 months in an account that pays 7% , compounded semi- annually. How much money will he have in the account in 4 years? 5,747.82 4,003 2,676.49 3,856
Ronald deposited 635 at the end of every 6 months in an account that pays 7% , compounded semi-
annually. How much money will he have in the account in 4 years?
 5,747.82
 4,003
 2,676.49
 3,856

Solution
3.8(237 votes)

Answer

\ 5,747.82 Explanation 1. Identify the formula for future value of an annuity Use the future value of an ordinary annuity formula: **FV = P \frac{(1 + r)^n - 1}{r}**, where P is the payment, r is the interest rate per period, and n is the total number of periods. 2. Determine values for the formula P = 635, r = \frac{7\%}{2} = 0.035, n = 4 \times 2 = 8 (since payments are semi-annual). 3. Calculate the future value Substitute the values into the formula: FV = 635 \frac{(1 + 0.035)^8 - 1}{0.035}. 4. Compute the result FV = 635 \frac{(1.035)^8 - 1}{0.035} = 635 \frac{1.3168 - 1}{0.035} = 635 \times 9.0514 \approx 5,747.82.

Explanation

1. Identify the formula for future value of an annuity<br /> Use the future value of an ordinary annuity formula: **$FV = P \frac{(1 + r)^n - 1}{r}$**, where $P$ is the payment, $r$ is the interest rate per period, and $n$ is the total number of periods.<br /><br />2. Determine values for the formula<br /> $P = 635$, $r = \frac{7\%}{2} = 0.035$, $n = 4 \times 2 = 8$ (since payments are semi-annual).<br /><br />3. Calculate the future value<br /> Substitute the values into the formula: $FV = 635 \frac{(1 + 0.035)^8 - 1}{0.035}$.<br /><br />4. Compute the result<br /> $FV = 635 \frac{(1.035)^8 - 1}{0.035} = 635 \frac{1.3168 - 1}{0.035} = 635 \times 9.0514 \approx 5,747.82$.
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