QuestionJune 12, 2025

a. Use the appropriate formula to find the value of the annuity. b. Find the interest. Periodic Deposit & Rate & Time 5000 at the end of each year & 5.5 % compounded annually & 15 years (i) Click the icon to view some finance formulas. a. The value of the annuity is square (Do not round until the final answer. Then round to the nearest dollar as needed.)

a. Use the appropriate formula to find the value of the annuity. b. Find the interest. Periodic Deposit & Rate & Time 5000 at the end of each year & 5.5 % compounded annually & 15 years (i) Click the icon to view some finance formulas. a. The value of the annuity is square (Do not round until the final answer. Then round to the nearest dollar as needed.)
a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.

 Periodic Deposit & Rate & Time 
  5000 at the end of each year & 5.5 % compounded annually & 15 years 


(i) Click the icon to view some finance formulas.
a. The value of the annuity is square 
(Do not round until the final answer. Then round to the nearest dollar as needed.)

Solution
4.4(302 votes)

Answer

a. The value of the annuity is \117,320. ### b. The interest earned is \42,320. Explanation 1. Identify the Annuity Formula Use the future value of an ordinary annuity formula: **FV = P \frac{(1 + r)^n - 1}{r}**, where ( ( \(P\) ) ) is the periodic deposit, ( ( \(r\) ) ) is the interest rate per period, and ( ( \(n\) ) ) is the number of periods. 2. Substitute Values into the Formula Given ( ( \(P = 5000\) ) ), ( ( \(r = 0.055\) ) ), and ( ( \(n = 15\) ) ). Substitute these values into the formula: \[ FV = 5000 \frac{(1 + 0.055)^{15} - 1}{0.055} \] 3. Calculate the Future Value Compute the expression: \[ (1 + 0.055)^{15} = 2.29057 \] \[ FV = 5000 \times \frac{2.29057 - 1}{0.055} \] \[ FV = 5000 \times \frac{1.29057}{0.055} \] \[ FV = 5000 \times 23.464 \] \[ FV = 117,320 \] 4. Calculate the Total Interest Earned Subtract the total deposits from the future value to find the interest: \[ \text{Total Deposits} = 5000 \times 15 = 75,000 \] \[ \text{Interest} = 117,320 - 75,000 = 42,320 \]

Explanation

1. Identify the Annuity Formula<br /> Use the future value of an ordinary annuity formula: **$FV = P \frac{(1 + r)^n - 1}{r}$**, where ( \(P\) ) is the periodic deposit, ( \(r\) ) is the interest rate per period, and ( \(n\) ) is the number of periods.<br /><br />2. Substitute Values into the Formula<br /> Given ( \(P = 5000\) ), ( \(r = 0.055\) ), and ( \(n = 15\) ). Substitute these values into the formula: <br />\[ FV = 5000 \frac{(1 + 0.055)^{15} - 1}{0.055} \]<br /><br />3. Calculate the Future Value<br /> Compute the expression:<br />\[ (1 + 0.055)^{15} = 2.29057 \]<br />\[ FV = 5000 \times \frac{2.29057 - 1}{0.055} \]<br />\[ FV = 5000 \times \frac{1.29057}{0.055} \]<br />\[ FV = 5000 \times 23.464 \]<br />\[ FV = 117,320 \]<br /><br />4. Calculate the Total Interest Earned<br /> Subtract the total deposits from the future value to find the interest:<br />\[ \text{Total Deposits} = 5000 \times 15 = 75,000 \]<br />\[ \text{Interest} = 117,320 - 75,000 = 42,320 \]
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