Calculate the time in which a capital of Q.12,000, placed at an interest of 5.5% capitalized semiannually it increases its value to Q13,000

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Answer to a math question Calculate the time in which a capital of Q.12,000, placed at an interest of 5.5% capitalized semiannually it increases its value to Q13,000

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A = P \left(1 + \frac{r}{n}\right)^{nt}

13000 = 12000 \left(1 + \frac{0.055}{2}\right)^{2t}

1 + \frac{0.055}{2} = 1.0275

13000 = 12000 \cdot 1.0275^{2t}

\frac{13000}{12000} = 1.0275^{2t}

1.0833 = 1.0275^{2t}

\ln(1.0833) = \ln(1.0275^{2t})

\ln(1.0833) = 2t \ln(1.0275)

t = \frac{\ln(1.0833)}{2 \ln(1.0275)}

t \approx 1.48 \text{ years}

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