Respuesta :
Suppose you invest $500
Principal Amount = $500
that pays 3.5% annual interest i.e.
Rate of Interest = 3.5%
Amount = $650
We need to find the time period
The general expression for the compund interest is :
[tex]\text{ Amount = Principal(}1+\frac{rate\text{ of interest}}{100})^{time}[/tex]Substitute the value and simplify :
[tex]\begin{gathered} \text{ Amount = Principal(}1+\frac{rate\text{ of interest}}{100})^{time} \\ 650=500(1+\frac{3.5}{100})^{time} \\ Divide\text{ both side by 500} \\ \frac{650}{500}=\frac{500}{500}(1+\frac{3.5}{100})^{time} \\ \frac{13}{10}=(1+\frac{3.5}{100})^{time} \\ Apply\text{ exponents rule:} \\ Time\text{ ln(1+}\frac{3.5}{100})=\ln \frac{13}{10} \\ Time\text{ ln(}\frac{103.5}{100})=\ln \frac{13}{10} \\ \text{Time = }\frac{\ln\frac{13}{10}}{\text{ln(}\frac{103.5}{100})} \\ \text{Time = }7.6266\text{ years} \\ \text{Time }\approx8years \end{gathered}[/tex]Time = 8 years
