QuestionAugust 18, 2025

A sum of money is invested at 12% compounded quarterly.About how long will it take for the amount of money to double? Compound interest formula: V(t)=P(1+(r)/(n))^nt t=years since initial deposit n=number of times compounded per year r=annual interest rate(as a decimal) P=initial (principal) investment V(t)=value of investment after tyears 5.9 years 6.1 years 23.4 years 24.5 years

A sum of money is invested at 12% compounded quarterly.About how long will it take for the amount of money to double? Compound interest formula: V(t)=P(1+(r)/(n))^nt t=years since initial deposit n=number of times compounded per year r=annual interest rate(as a decimal) P=initial (principal) investment V(t)=value of investment after tyears 5.9 years 6.1 years 23.4 years 24.5 years
A sum of money is invested at 12% compounded quarterly.About how long will it take for the amount of money to double? Compound interest formula: V(t)=P(1+(r)/(n))^nt t=years since initial deposit n=number of times compounded per year r=annual interest rate(as a decimal) P=initial (principal) investment V(t)=value of investment after tyears 5.9 years 6.1 years 23.4 years 24.5 years

Solution
4.5(349 votes)

Answer

5.9 years Explanation 1. Set up the equation Use V(t) = P(1 + \frac{r}{n})^{nt} with V(t) = 2P, r = 0.12, n = 4. 2. Solve for t 2 = (1 + \frac{0.12}{4})^{4t}. Simplify to 2 = (1.03)^{4t}. 3. Apply logarithms \log(2) = 4t \cdot \log(1.03). 4. Calculate t t = \frac{\log(2)}{4 \cdot \log(1.03)}.

Explanation

1. Set up the equation<br /> Use $V(t) = P(1 + \frac{r}{n})^{nt}$ with $V(t) = 2P$, $r = 0.12$, $n = 4$.<br />2. Solve for $t$<br /> $2 = (1 + \frac{0.12}{4})^{4t}$. Simplify to $2 = (1.03)^{4t}$.<br />3. Apply logarithms<br /> $\log(2) = 4t \cdot \log(1.03)$.<br />4. Calculate $t$<br /> $t = \frac{\log(2)}{4 \cdot \log(1.03)}$.
Click to rate:

Similar Questions