An investor took out a loan of 150,000 at 8% compounded quarterly, to be repaid over 10 years with quarterly payments of 5483.36 at the end of each quarter. after 12 payments, the interest rate dropped to 6% compounded quarterly. the new quarterly payment dropped to 5134.62. after 20 payments in total, the interest rate on the loan increased to 7% compounded quarterly. the investor decided to make an additional payment of x at the time of his 20th payment. after the additional payment was made, the new quarterly payment was calculated to be 4265.73, payable for five more years. determine x.

Lavage rapide is a canadian company that owns and operates a large automatic car wash facility near montreal. the following table provides data concerning the company’s costs: fixed cost per month cost per car washed cleaning supplies $ 0.70 electricity $ 1,400 $ 0.07 maintenance $ 0.15 wages and salaries $ 4,900 $ 0.30 depreciation $ 8,300 rent $ 1,900 administrative expenses $ 1,400 $ 0.03 for example, electricity costs are $1,400 per month plus $0.07 per car washed. the company expects to wash 8,000 cars in august and to collect an average of $6.50 per car washed. the actual operating results for august appear below. lavage rapide income statement for the month ended august 31 actual cars washed 8,100 revenue $ 54,100 expenses: cleaning supplies 6,100 electricity 1,930 maintenance 1,440 wages and salaries 7,660 depreciation 8,300 rent 2,100 administrative expenses 1,540 total expense 29,070 net operating income $ 25,030 required: calculate the company's revenue and spending variances for august.