Final answer:
To solve for 'x' in the compound interest problem presented, we used the compound interest formula. After setting up the equation (2x + 5,000)(1.25)^2 - (2x + 5,000) = 7x + 7,800 and simplifying, we solved for 'x' and found that x = -0.85.
Step-by-step explanation:
To find the value of 'x' in the compound interest problem given, we need to apply the formula for the calculation of compound interest over two years. The formula for compound interest is A = P(1 + r/n)nt, where A is the amount after time t, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Ritika's investment is compounded annually, so n will be 1.
The equation representing the situation is:
P(1 + r)t - P = Interest
So we have, (2x + 5,000)(1 + 0.25)2 - (2x + 5,000) = 7x + 7,800. Expanding this equation, we simplify and solve for 'x' to find its value. Remember that the compound interest earned is represented by the branch of the equation that calculates the total amount after interest minus the original principal.
Simplifying the values:
- (2x + 5,000)(1.25)2 - (2x + 5,000) = 7x + 7,800
- (2x + 5,000)(1.5625) - (2x + 5,000) = 7x + 7,800
- 3,125x + 7,812.5 - 2x - 5,000 = 7x + 7,800
- 1,125x + 2,812.5 = 7x + 7,800
- 1,125x - 7x = 7,800 - 2,812.5
- -5,875x = 4,987.5
- x = -4,987.5 / 5,875
- x = -0.85
Therefore, the value of 'x' that satisfies the given condition is -0.85.