Question

You want to invest $1000 in an account and plan to leave it there for 12 years. There are three options for investing your money.Account A pays 14% interest per year, compounded annually.Account B pays 13.6% interest per year, compounded monthly.Account C pays 13% interest per year, compounded daily.

Answer 1

`\begin{gathered} Investment\text{ = \$}1000 \\ Account\text{ A} \\ i=14\text{ \%=0.14} \\ t=12\text{ years} \\ C=1000(1+0.14)^(12) \\ C=4871.9 \\ \text{After 12 years, youll have \$4871,9} \\ \text{Account B} \\ i=13.6\text{\%=0.136},\text{ monthly},\text{ hence} \\ i=(0.136)/(12)\approx0.0113 \\ t=\text{ 12 years}\cdot(12month)/(year)=144\text{ months} \\ C=1000(1+0.0113)^(144) \\ C=5043.37 \\ \text{After 12 years, youll have \$5}043.37 \\ \text{Account C} \\ i=13\text{\%=0.13, da}ily,\text{ hence} \\ i=(0.13)/(365)\approx0.00036 \\ t=12\text{ years}\cdot\frac{365\text{ days}}{years}=4380 \\ C=1000(1+0.00036)^(4380) \\ C=4838.07 \\ \text{After 12 years, youll have \$4838.07} \end{gathered}`