You would like to buy a new home theater system, which costs $1, 700 now. As a result your savings, you now have a sum equivalent to 60% of the system's current price. Since this money is not enough, you are planning to invest it so as to buy the home theater in the future. Moreover, during the next 12 months, you are planning to save an additional $50 per month toward this purchase (savings occur at the end of the month).1 You will earn an APR of 9% (compounded monthly) on all your savings. The price of the home theater will also increase at the rate of x% per month.
If your total savings will be exactly equal to the price of the theater in 12 months, what is the rate of the monthly increase in the price of the home theater, x?