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Li Ting deposits $20 000 in a bank that pays a simple interest rate of 2.75% per annum. (i) Find the amount of interest she earns every year.

If the interest rate decreases to x% per annum, she will receive $50 less every year. (ii) Find the value of x. ​

User Tolsto
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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.

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