You purchase a home and secure a 30 year equal payment loan for $200,000 at a interest rate of 5.25% apr compounded monthly. after 5 years the interest rate drops to 4.75% apr compounded monthly. the bank is charging 2 points to originate the new loan. how many months do you need to stay in the house after the refinance to make the refinance a benefit (round to next month)?

Emily spent her summer vacation in buenos aires, argentina, where she got plastic surgery for a fraction of what it would cost in the united states. this is an example of:

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?

Suppose a country's productivity last year was 84. if this country's productivity growth rate of 5 percent is to be maintained, this means that this year's productivity will have to be: