With an initial investment of $100, I invest $500 per year, continuously, at an interest rate of 5%, leaving the money in the bank. Assuming the interest is compounded continuously, the initial value problem which describes the amount $S in the bank t years later is given by:

Winners of the georgia lotto drawing are given the choice of receiving the winning amount divided equally over 2121 years or as a lump-sum cash option amount. the cash option amount is determined by discounting the annual winning payment at 88% over 2121 years. this week the lottery is worth $1616 million to a single winner. what would the cash option payout be?

Palmer frosted flakes company offers its customers a pottery cereal bowl if they send in 3 boxtops from palmer frosted flakes boxes and $1. the company estimates that 60% of the boxtops will be redeemed. in 2012, the company sold 675,000 boxes of frosted flakes and customers redeemed 330,000 boxtops receiving 110,000 bowls. if the bowls cost palmer company $3 each, how much liability for outstanding premiums should be recorded at the end of 2012?

Anew firm is developing its business plan. it will require $615,000 of assets, and it projects $450,000 of sales and $355,000 of operating costs for the first year. management is reasonably sure of these numbers because of contracts with its customers and suppliers. it can borrow at a rate of 7.5%, but the bank requires it to have a tie of at least 4.0, and if the tie falls below this level the bank will call in the loan and the firm will go bankrupt. what is the maximum debt ratio the firm can use? (hint: find the maximum dollars of interest, then the debt that produces that interest, and then the related debt ratio.)a. 41.94%b. 44.15%c. 46.47%d. 48.92%e. 51.49%