Can you please help me answer these questions.
1. The balance in your saving account on 01/01/2013 was $12,000. On 01/01/2016 you check the balance again, and it is $12,894. The bank computes the interest rate compounded monthly. What is the interest rate per month? (Hint 1: First, find how many months there are between two dates. Note the question is asking the interest rate per month, not per year. Solve for the r using
2. How many years would it take for you to double your initial deposit? The interest rate is 4%/year, compounded annually. You make a deposit only once in the beginning. You may round the final answer to the nearest hundredth. For example, just write down 3.41 years if the true answer were 3.4123. (Hint: Let $C denote the initial deposit. Then, the future value will be $2C someday. Find how many years you should wait until such day comes finally, using the future value formula. You can do it by trial and error or by using log(2) and log(1.04). If you don't know the logarithm, just do it by trial and error. When you do it by trial and error, you can replace $C by any dollar amounts (say $1), and your answer will be still the same because $C will be cancelled out during calculation anyway.)