Kevin kept his money in XYZ bank. His cash quadrupled in 2 years at a rate of x% compounded annually. What is the value of x? Ops: A. 50 B. 200 C. 100 D. 80
Question
Kevin kept his money in XYZ bank. His cash quadrupled in 2 years at a rate of x% compounded annually. What is the value of x? Ops: A. 50 B. 200 C. 100 D. 80
Solution
To solve this problem, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, Kevin's cash quadrupled, so A = 4P. The money was kept for 2 years, so t = 2. The interest was compounded annually, so n = 1. We need to find r, the annual interest rate.
Substituting the given values into the formula, we get:
4P = P(1 + r/1)^(1*2) 4 = (1 + r)^2
Taking the square root of both sides to solve for r, we get:
2 = 1 + r r = 2 - 1 r = 1
So, the annual interest rate is 1, or 100% when expressed as a percentage. Therefore, the value of x is 100.
So, the answer is C. 100.
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