lisa mcneil needs to choose between two investments: one pays 9.8% compounded continuously, and the other…

Explanation:

Step1: Calculate the future - value for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $P=$10000$, $r = 0.098$, and $t = 2$. $A_1=10000\times e^{0.098\times2}$ $A_1 = 10000\times e^{0.196}$ $A_1\approx10000\times1.216097\approx$12160.97$ The interest earned $I_1=A_1 - P=12160.97 - 10000=$2160.97$

Step2: Calculate the future - value for compounding quarterly

The formula for compound interest is $A=P(1 + \frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years. Given $P = 10000$, $r=0.10$, $n = 4$ (compounded quarterly), and $t = 2$. $A_2=10000\times(1+\frac{0.10}{4})^{4\times2}$ $A_2=10000\times(1 + 0.025)^{8}$ $A_2=10000\times1.025^{8}$ $A_2=10000\times1.218403\approx$12184.03$ The interest earned $I_2=A_2 - P=12184.03 - 10000=$2184.03$

Step3: Compare the interests

Since $I_2>I_1$, she should choose the investment that pays 10% compounded quarterly. The extra interest $=I_2 - I_1=2184.03 - 2160.97=$23.06$

Answer:

She should choose the 10% compounded quarterly investment. She will earn $$23.06$ extra interest using this choice.