QuestionMay 24, 2025

Question 32(1 point) Solve the problem. How long, to the nearest tenth of a year, will it take for a 3200 investment to double if i invested at 9% compounded quarterly? Use the formula A=P(1+(r)/(n))^nt 8 yr 7.8 yr 8.2 yr d 7.6 yr

Question 32(1 point) Solve the problem. How long, to the nearest tenth of a year, will it take for a 3200 investment to double if i invested at 9% compounded quarterly? Use the formula A=P(1+(r)/(n))^nt 8 yr 7.8 yr 8.2 yr d 7.6 yr
Question 32(1 point) Solve the problem. How long, to the nearest tenth of a year, will it take for a 3200 investment to double if i invested at 9% compounded quarterly? Use the formula A=P(1+(r)/(n))^nt 8 yr 7.8 yr 8.2 yr d 7.6 yr

Solution
4.7(328 votes)

Answer

7.8 yr Explanation 1. Identify Variables P = 3200, A = 6400 (since the investment doubles), r = 0.09, n = 4. 2. Apply Compound Interest Formula Use A = P(1+\frac{r}{n})^{nt}, substitute known values: 6400 = 3200(1+\frac{0.09}{4})^{4t}. 3. Simplify Equation Divide both sides by 3200: 2 = (1+\frac{0.09}{4})^{4t}. 4. Calculate Base Value Compute base value: 1+\frac{0.09}{4} = 1.0225. 5. Solve for t Take logarithm of both sides: \log(2) = 4t \cdot \log(1.0225). Solve for t: t = \frac{\log(2)}{4 \cdot \log(1.0225)}. 6. Compute t Calculate t: t \approx \frac{0.3010}{4 \times 0.0097} \approx 7.8.

Explanation

1. Identify Variables<br /> $P = 3200$, $A = 6400$ (since the investment doubles), $r = 0.09$, $n = 4$.<br /><br />2. Apply Compound Interest Formula<br /> Use $A = P(1+\frac{r}{n})^{nt}$, substitute known values: $6400 = 3200(1+\frac{0.09}{4})^{4t}$.<br /><br />3. Simplify Equation<br /> Divide both sides by 3200: $2 = (1+\frac{0.09}{4})^{4t}$.<br /><br />4. Calculate Base Value<br /> Compute base value: $1+\frac{0.09}{4} = 1.0225$.<br /><br />5. Solve for $t$<br /> Take logarithm of both sides: $\log(2) = 4t \cdot \log(1.0225)$.<br /> Solve for $t$: $t = \frac{\log(2)}{4 \cdot \log(1.0225)}$.<br /><br />6. Compute $t$<br /> Calculate $t$: $t \approx \frac{0.3010}{4 \times 0.0097} \approx 7.8$.
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