Get personalized answers to your unique questions on IDNLearn.com. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.
Sagot :
[tex]\begin{gathered} \text{ Given} \\ A=290250 \\ r=0.114\text{ converted from percentage} \\ n=12,\text{ since it is compounded monthly (12 months in a year)} \\ A=P(1+\frac{r}{n})^{nt}\rightarrow\text{Compound Interest Formula} \\ \text{ A.) Substitute all the following values, that should leave us with} \\ \text{ P and t as variables} \\ A=P(1+\frac{r}{n})^{nt} \\ 290250=P(1+\frac{0.114}{12})^{12t}\rightarrow290250=P(1.0095)^{12t} \\ \text{ B.) Solve the equation for P} \\ \text{ We isolate P on the left hand side and we get} \\ 290250=P(1.0095)^{12t} \\ P(1.0095)^{12t}=290250 \\ \frac{P\cancel{(1.0095)^{12t}}}{\cancel{(1.0095)^{12t}}}=\frac{290250}{(1.0095)^{12t}} \\ P=\frac{290250}{(1.0095)^{12t}} \\ \text{ C.) Solve for t} \\ 290250=P(1.0095)^{12t} \\ P(1.0095)^{12t}=290250 \\ \frac{\cancel{P}(1.0095)^{12t}}{\cancel{P}}=\frac{290250}{P} \\ 1.0095^{12t}=\frac{290250}{P}\text{ get the natural logarithm of both sides} \\ \ln (1.0095^{12t})=\ln \frac{290250}{P} \\ 12t\cdot\ln 1.0095=\ln \frac{290250}{P},\text{ after this divide both sides by 12 and ln (1.0095)} \\ \text{ to isolate }t \\ \frac{\cancel{12}t\cdot\cancel{\ln (1.0095)}}{\cancel{12\cdot\ln(1.0095)}}=\frac{\ln\frac{290250}{P}}{12\cdot\ln(1.0095)} \\ t=\frac{\ln\frac{290250}{P}}{12\cdot\ln(1.0095)} \\ \text{ D.) Using the equation that we have on B, just substitute the values} \\ \text{ with }t=17 \\ P=\frac{290250}{(1.0095)^{12t}} \\ P=\frac{290250}{(1.0095)^{12(17)}} \\ \text{ Input this in a calculator and we get} \\ P=\$42177.64 \\ \text{ E.) Using the equation that have on C, substitute the values with} \\ P=135000 \\ t=\frac{\ln\frac{290250}{P}}{12\cdot\ln(1.0095)} \\ t=\frac{\ln \frac{290250}{135000}}{12\cdot\ln (1.0095)} \\ \text{ Input this in a calculator and we get} \\ t=6.75\text{ years},\text{ rounded to a hundredth} \end{gathered}[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.
