Please answer all questions. Thank you. 
Carlos invested $5,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 months ( 245 days) was $5,140.89. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year). (Round your answer to two decimal places.) % Use logarithms to solve the problem. The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years. (a) Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously. yr (b) What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.) (3) Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.) The Pirerras are planning to go to Europe 4 years from now and have agreed to set aside $170/month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 3%/y year compounded monthly, how much money will be in their travel fund at the end of the fourth year? (Round your answer to the nearest cent.) $ Lauren plans to deposit $5000 into a bank account at the beginning of next month and $200/ month into the same account at the end of that month and at the end of each subsequent month for the next 5 years. If her bank pays interest at a rate of 5%/ year compounded monthly, how much will Lauren have in her account at the end of 5 years? (Assume she makes no withdrawals during the 5-year period. Round your answer to the nearest cent.) From age 25 to age 40 , Jessica deposited $200 at the end of each month into a tax-free retirement account. She made no withdrawals or further contributions until age 65 . Alex made monthly deposits of $300 into his tax-free retirement account from age 40 to 65 . If both accounts earned interest at the rate of 7%/y yar compounded monthly, who ends up with the bigger nest egg upon reaching the age of 65 ? Hint: Use both the annuity formula and the compound interest formula. Jessica Alex Find the present value of the ordinary annuity. (Round your answer to the nearest cent.) $130/ month for 14 years at 4%/ year compounded monthly Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 2.5%/y ear compounded monthly. If the future value of the annuity after 13 years is $75,000, what was the size of each payment? (Round your answer to the nearest cent.) $ The management of Gibraltar Brokerage Services anticipates a capital expenditure of $28,000 in 3 years for the purchase of new computers and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of 3%/y ear compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund. (Round your answer to the nearest cent.) $ Since he was 21 years old, Ben has been depositing $200 at the end of each month into a tax-free retirement account earning interest at the rate of 2.5%/ year compounded monthly. Larry, who is the same age as Ben, decided to open a tax-free retirement account 5 years after Ben opened his. If Larry's account earns interest at the same rate as Ben's, determine how much Larry should deposit each month into his account so that both men will have the same amount of money in their accounts at aqe 65 . (Round your answer to the nearest cent.)
