Raj deposits $20000 in the bank that pays simple interest at the rate of 2.75% at anuum. If the interest rate decrease to x%. He will receive $50 less every year. Find the value of x?
The easy way: $50 = 0.25% of 20,000
So, his interest rate was 2.75 - 0.25 = 2.5%
Or, algebraically,
20000(1.0275 - (1+x/100)) = 50
x = 2.5
Can you tell the formula
To find the value of x, let's assume that the initial interest rate is 2.75%.
Let's calculate the amount of interest Raj receives with the initial interest rate.
Simple Interest (SI) = (Principal * Rate * Time) / 100
SI = (20000 * 2.75 * 1) / 100
SI = 550 / 100
SI = $550
Now we know that Raj receives $550 interest every year at an interest rate of 2.75%.
Let's say the interest rate decreases to x%.
We are given that if the interest rate decreases to x%, Raj will receive $50 less every year.
So, Raj will receive $550 - $50 = $500 interest every year at the interest rate of x%.
Now, let's solve for x:
(SI with 2.75% interest) - (SI with x% interest) = $50
550 - (20000 * x * 1) / 100 = 50
550 - 200x = 50
200x = 550 - 50
200x = 500
x = 500 / 200
x = 2.5
Therefore, when the interest rate decreases to 2.5%, Raj will receive $50 less every year.
To find the value of x, we can set up an equation based on the given information.
Let's denote the original interest rate as 2.75% (or 0.0275 as a decimal). Raj receives $50 less each year when the interest rate decreases to x%.
The interest earned each year can be calculated using the formula:
Interest = Principal * Rate
So, for the original interest rate, the interest earned each year is:
0.0275 * $20,000 = $550
Now, for the decreased interest rate of x%, the interest earned each year is:
(x/100) * $20,000 = ($20,000x/100) = $20x
According to the given information, when the interest rate decreases, Raj will receive $50 less each year. Therefore, we can set up the following equation:
$550 - $20x = $50
We can now solve this equation to find the value of x.
$550 - $20x = $50
Subtracting $50 from both sides:
$500 - $20x = 0
Dividing both sides by $20:
$25 - x = 0
Rearranging the equation:
x - $25 = 0
Adding $25 to both sides:
x = $25
Therefore, the value of x is 25%. When the interest rate decreases to 25%, Raj will receive $50 less every year.