QuestionAugust 21, 2025

7. Marcy placed 3,000 each year into an investment returning 9 percent a year for her daughter's college education. She started when her daughter was two . How much had she accumulated by her daughter's 18th birthday?

7. Marcy placed 3,000 each year into an investment returning 9 percent a year for her daughter's college education. She started when her daughter was two . How much had she accumulated by her daughter's 18th birthday?
7. Marcy placed 3,000 each year into an investment returning 9 percent a year for her
daughter's college education. She started when her daughter was two . How much had
she accumulated by her daughter's 18th birthday?

Solution
4.5(111 votes)

Answer

\102,453.30 Explanation 1. Identify the Investment Period Marcy invests for 16 years (from age 2 to 18). 2. Use Future Value of Annuity Formula The future value of an annuity formula is **FV = P \times \frac{(1 + r)^n - 1}{r}**, where P = 3000, r = 0.09, and n = 16. 3. Calculate Future Value Substitute the values into the formula: FV = 3000 \times \frac{(1 + 0.09)^{16} - 1}{0.09}. 4. Compute the Result Calculate: FV = 3000 \times \frac{(1.09)^{16} - 1}{0.09} = 3000 \times \frac{4.0736 - 1}{0.09} = 3000 \times 34.1511. 5. Final Calculation FV = 102,453.30.

Explanation

1. Identify the Investment Period<br /> Marcy invests for 16 years (from age 2 to 18).<br /><br />2. Use Future Value of Annuity Formula<br /> The future value of an annuity formula is **$FV = P \times \frac{(1 + r)^n - 1}{r}$**, where $P = 3000$, $r = 0.09$, and $n = 16$.<br /><br />3. Calculate Future Value<br /> Substitute the values into the formula: $FV = 3000 \times \frac{(1 + 0.09)^{16} - 1}{0.09}$.<br /><br />4. Compute the Result<br /> Calculate: $FV = 3000 \times \frac{(1.09)^{16} - 1}{0.09} = 3000 \times \frac{4.0736 - 1}{0.09} = 3000 \times 34.1511$.<br /><br />5. Final Calculation<br /> $FV = 102,453.30$.
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