Business Mathematics – Summer 2025 – Midterm

1. (a) Explain annuity, compound interest and amortization. 3 (b) Interpret the property of equilateral triangle and right-angled triangle. 2 2. (a) A landowner wants to make a small triangular garden. The three corners of the garden will be at points (3, 6), (x, 0), and (6, –4) on a map. The garden must have an area of exactly 29 square meters. Identify the value of x that makes the area of this triangle 29 square meters. 2.5 (b) Michael opens a savings account and deposits $5,000. After 2 years, the total amount in his account grows to $5,600. Assuming the bank pays simple interest, choose the annual interest rate offered by the bank. 2.5 3. (a) Solve the following equation: log_x 2 + log_x 9 + log_x 12 = 3 2.5 (b) If log ((x+y)/9) = (1/2) (log x + log y) then show that x/y + y/x = 79 2.5 4. (a) Identify the number of months it will take at 9 percent interest compounded semi-annually for $5,000 to grow to $10,000. 2.5 (b) A hospital wants to set up a medical equipment replacement fund by depositing a fixed amount at the end of every three months into a reserve account. The goal is to accumulate $120,000 in 7 years. If the fund earns 7% interest compounded quarterly, select the value should be transferred in each deposit. 2.5 5. (a) Identify the value of k that the points (2, 3/2), (–3, –7/2) and (k, 9/2) are on the same line. 2 (b) Examine that the points A(6, 6), B(2, 3) and C(4, 7) are the vertices of right-angled triangle or not. 3