Question # Find the value and interest earned if $8906.54 is invested for 9 years at % compounded a) semiannually b) continuosly Modeling data distributions ANSWERED asked 2020-11-29 Find the value and interest earned if$8906.54 is invested for 9 years at $$\%$$ compounded
a) semiannually
b) continuosly 2020-11-30
a) The future value for the amount $8906.54 for 9years at $$3\%$$ compounded semiannually is calculated a follows. $$\displaystyle{A}={P}{\left({1}+\frac{r}{{2}}\right)}^{2}{t}{\left(\text{semiannually}\right)}$$ $$\displaystyle{A}={8906.4}{\left({1}+\frac{0.03}{{2}}\right)}^{{{\left({2}\cdot{9}\right)}}}$$ $$\displaystyle=\{11643.88}$$ b) The future value for the amount$8906.54 for 9years at $$3\%$$ compounded continuously is calculated a follows.
Future value $$\displaystyle={A}{e}^{r}{t}$$
$$\displaystyle={\left({8906.54}\right)}{e}^{{{\left({0.03}\right)}{\left({9}\right)}}}$$
$$\displaystyle=\{11667.25}$$
Interest earned $$\displaystyle={A}-{P}$$
$$\displaystyle={11667.25}-{8906.54}$$
$$\displaystyle=\{2760.71}$$