need help with number 46

35. \\( \\$ 55,000 \\); monthly payments for 12 years; interest rate \5.7 36. \\( \\$ 125,000 \\); monthly payments for 9 years; interest rate \6 37. Cigarette Costs The website www.theawl.com estimates that a pack-a-day smoker in New York State spends \\( \\$ 400 \\) a month on cigarettes (the highest cost of the 50 states). Suppose the smoker invests that amount at the end of each month in a money market account that pays \.85 interest compounded monthly. What would the account be worth after 30 years? 38. Cigarette Costs The website www.theawl.com estimates that a pack-a-day smoker in Virginia spends \\( \\$ 150 \\) a month on cigarettes (the lowest cost of the 50 states). Suppose the smoker invests that amount at the end of each month in a money market account that pays \.85 interest compounded monthly. What would the account be worth after 30 years? 39. Investing Mary Dodge deposits \\( \\$ 12,000 \\) at the end of each year for 9 years in an investment account with a guaranteed interest rate of \6 compounded annually. (a) Find the value of the account at the end of the 9 years. (b) Mary's sister works for an investment firm that pays \5 compounded annually. If Mary deposits money with this account, what is the value of the account when Mig reaches age 65 ? 43. Investing A mother opened an investment account for son on the day he was born, investing \\$1000. Each year on birthday, she deposits another \\( \\$ 1000 \\), making the last deposit his 18 th birthday. If the account paid a return rate of \5.6 col pounded annually, how much is in the account at the end of \\( t \\) day on the son's 18th birthday? 44. Investing A grandmother opens an investment account for he onily granddaughter on the day she was born, investing \\( \\$ 50 \\mathrm{C} \\) Each year on her birthday, she deposits another \\( \\$ 500 \\), makin the last deposit on her 25 th birthday. If the account paid a retur rate of \6.2 compounded annually, how much is in the accoun at the end of the day on the granddaughter's 25 th birthday? 45. Investing Chuck Hickman deposits \\( \\$ 10,000 \\) at the beginning of each year for 12 years in an account paying \5 compounded annually. He then puts the total amount on deposit in another account paying \6 compounded semiannually for another 9 years. Find the final amount on deposit after the entire 21-year period. 46. Investing Suppose that the best rate that the company in Example 6 can find is \6.3, compounded monthly (rather than the \6.661 it wants). Then the company must deposit more in the sinking fund each month. What monthly deposit will guarantee that the fund will be worth \\( \\$ 100,000 \\) in 20 years? 47. Investing Diego Sanchez needs \\( \\$ 10,000 \\) in 8 years. (a) What amount should he deposit at the end of each quarter at \5 compounded quarterly so that he will have his \\( \\$ 10,000 \\) ? (b) Find Diego's quarterly deposit if the money is deposited at \5.8 compounded quarterly