Theory question 113
Commercial Arithmetic(a) On Sam's first birthday celebration, his grandfather deposited an amount of $1,000.00 in a bank compounded at 4% interest annually. Find how much is in the account if Sam is 4 years old.
(b) In the diagram, ABCD are points on the circle centre O. If |AB| = |BC| and ∠ADC = 50°, find ∠BAD.
Show the model answer
Model answer
(a) From age 1 to age 4 is 3 years
Amount = 1,000 × (1.04)3 = $1,124.86
(b) ∠ABC = 180° − 50° = 130° (opposite angles of cyclic quadrilateral)
AB = BC → ∠BAC = (180° − 130°)/2 = 25°
AD is a diameter → ∠ACD = 90°, so ∠CAD = 180° − 90° − 50° = 40°
∠BAD = 25° + 40° = 65°
Explanation
Count the years from the first birthday, not from birth.