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For full credit please show all your work and explain your answers 1. You deposit $3,000 in a savings account. a. How many years do you need to double your money if your account earns 9% simple interest (not compounded) per year? b. If you deposit the $3,000 in another savings account that earns 8% interest, compounded yearly, how many years will take to double your money? 2. You are considering investing $1,000 at interest rate of 6%, compounded annually. for 5 years or investing the $1,000 at 7% per year simple interest rate for 5 years. Which option is better? . Suppose you have the option of receiving either $10,000 at the end of 5 years or dollars today. Currently you have no need for money, so you would deposit the P dollars in a bank that pays 6% interest, what value of P would make you indifferent in your choice between P dollars today and the promise of $10,000 at the end of 5 years? 4. You can buy a machine for $100,000 that will produce a net income, after operating expenses, of $10,000 per year. If you plan to keep the machine for four years, what must the market (resale) value be at the end of four years to justify the investment? Assume 15% annual return on the investment (interest rate). 5. The Rule of 72 can be used to find (approximately) the time required to double an investment for a given interest rate. The rule is as follows: Rule of 72: The time required to double the value of a lump-sum investment that is allowed to compound is approximately 72 divided by the annual interest rate (as a %) Use the Rule of 72 to determine how long it takes to accumulate $10,000 in a savings account when P-$5,000 and i-10% per year. Find the actual value using the appropriate formula and compare the two results