When a loan is paid off early, a portion of the finance charge must be
returned to the borrower. By one method of calculating the finance charge, the amount of
unearned interest (finance charge to be returned) is given by
Where u represents unearned interest, f is the original finance charge, n is the
number of payments remaining when the loan is paid off, and q is the original number of
payments. Find the amount of the unearned interest in this case below.
Original finance charge = $1400, loan scheduled to run 48 months, paid
off with 12 payments remaining.
Maria Matinelli brought two plots of land for a total of $120,000. On the
first plot she made a profit of 15%. On the second, she lost 10%. Her total profit was
How much did she pay for each piece of land?
Let x = the amount of money she spent on the first parcel.
Price of the second parcel = 120,000 - x.
15% profit on the sale of the first parcel, so she sold it for x and 15% of x, or 1.15x.
She lost 10% on the second parcel, so she sold it for only 90% of her purchase price, or
0.9(120,000 - x).
1.15x + 0.9(120,000 – x)
1.15x + 108,000 - 0.9x.
1.15x-0.9x + 108,000
0.25x + 108,000.
$5500 more than her purchase price of 120,000, so this amount equals 120,000 + 5500:
0.25x + 108,000 = 120,000 + 5500
0.25x + 108,000 = 125,500
0.25x = 17,500
x = $70,000 for first land
Second land is 120,000-x
120,000-70,000 = 50,000
$50,000 for second land
Jack borrowed his father’s luxury car and promised to return it with a full
tank of premium gas, which costs $2.50 per gallon. From experience he knows that he
needs 15.5 gallons. But he has only $38 (and no credit card) which isn’t enough. He
decides to get as much premium as possible and fill the remainder of the tank with
regular gas which costs $2.30 per gallon. How much of each type of gas should he get?