(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 ...

(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.

In the diagram, ABCD are points on the circle centre O. If |AB| = |BC| and ∠ADC= 50°, find ∠BAD.

(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° 

Answer Details

(a) If Sam's grandfather deposited $1,000.00 in a bank at 4% interest annually, after 4 years, the total amount in the account would be $1,124.86.

(b) To find ∠BAD, we need to find ∠CAD and ∠BAC first. We know that ∠ADC = 50° and ∠ADC + ∠DCA + ∠CAD = 180°, so ∠CAD = 180° - 50° - 90° = 40°. Next, we know that ∠ADC + ∠ABC = 180°, so ∠ABC = 180° - 50° = 130°. Also, ∠BAC + ∠BCA + ∠ABC = 180° and ∠BAC = ∠BCA, so 2∠BAC + 130° = 180° and ∠BAC = (180° - 130°) / 2 = 25°. Finally, ∠BAD = ∠CAD + ∠BAC = 40° + 25° = 65°.