(a) On Sam’s first birthday celebration, his grandfather deposited an amount of S 1,000.00 in a bank compound at 4 % interest annually.
Find how much is in the account if Sam is 4 years old.
(b) In the diagram above, ABCD are points on the circle centre O. If |AB| = |BC| and ∠ADC= 50°, find ∠BAD.
Explanation
(a) Amount at end of the 2nd year = \(\frac{104}{100}\) x $1000
= $1,040.00
Amount at end of 3rd year = \(\frac{104}{100}\) x $1040
= $1,081.60
Amount at end of 4th year = \(\frac{104}{100}\) x $1081.6
= $1,124.86
(b) ∠ADC + ∠DCA+ ∠CAD = 180°
50° + 90°+ ∠CAD = 180°
∠CAD = (180 - 140)°
= 40
∠ADC + ∠ABC = 180°
50° + ∠ABC = 180°
∠ABC =130°
∠BAC+ ∠BCA + ∠ABC = 180°
But ∠BAC = ∠BCA
2∠BAC+ ∠130° = 180°
2 ∠BAC=50°
∠BAC = 25°
∠BAD = ∠CAD + ∠BAC
= 40°+25° = 65°