Answer and Step-by-step explanation:
(i) To find the amount of interest Li Ting earns every year, we can use the formula for simple interest:
Interest = Principal × Rate × Time
In this case, the principal (P) is $20,000 and the rate (R) is 2.75% per annum. We need to convert the rate to a decimal by dividing it by 100:
R = 2.75% / 100 = 0.0275
Let's assume the time (T) is 1 year:
Interest = $20,000 × 0.0275 × 1
Therefore, Li Ting earns $550 in interest every year.
(ii) Now, let's find the value of x when the interest rate decreases by x% per annum. We know that when the interest rate decreases by x%, Li Ting receives $50 less in interest every year.
Using the same formula for simple interest:
Interest = Principal × Rate × Time
Let's assume the new rate (R') is (2.75% - x%) per annum. Again, we need to convert the rate to a decimal:
R' = (2.75% - x%) / 100 = (0.0275 - 0.01x)
We know that the interest decreases by $50, so we have:
$550 - $50 = $20,000 × (0.0275 - 0.01x) × 1
$500 = $20,000 × (0.0275 - 0.01x)
Simplifying the equation:
0.0275 - 0.01x = 0.025
-0.01x = 0.025 - 0.0275
-0.01x = -0.0025
Dividing both sides by -0.01:
x = -0.0025 / -0.01
x = 0.25
Therefore, the value of x is 0.25, which means the interest rate decreases by 0.25% per annum.