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Part A - Investment (Show all work.) You invest \\( \\$ 3000 \\) in a money market account that earns an annual interest rate of \4. 1. How much money would you have in the account at the end of 1 year? (This is known as simple interest.) 2. Suppose instead that you left your money in this money market account for a total of 10 years. How much money would you have in the account at the end of 10 years? (Keep in mind that interest compounds each year.) Compound Interest Formula: \\( \\boldsymbol{A}=\\boldsymbol{P}\\left(1+\\frac{r}{n}\ ight)^{n t} \\) 3. Often interest is calculated more often than just at the end of each year. Suppose instead that interest was calculated and added to the account at the end of each month. How much money would be in the account after 10 years given that interest is compounded monthly? 4. How much money would be in the account after 10 years given that interest is compounded daily? If interest could be compounded continuously, the compound interest formula converges (as \\( n \ ightarrow \\) \\( \\infty \\) ) to the formula \\( A=P e^{r t} \\). 5. How much money would be in the account after 10 years given that interest is compounded continuously? 6. Still using continuously compounded interest, how long would it take for the \\( \\$ 3000 \\) investment to reach \\( \\$ 4500 \\) ? (Solve using logarithms to find \\( t \\).) 7. Still using continuously compounded interest, how long would it take for the \\( \\$ 3000 \\) investment to double, i.e., reach \\( \\$ 6000 \\) ? (Solve using logarithms to find \\( t \\).) 8. Still using continuously compounded interest, how much money would be in the account after 50 years

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