Grace makes an initial deposit of x dollars into a savings account with a z percent interest rate, compounded annually. On the same day, Georgia makes an initial deposit of y dollars into a savings account with a z percent annual interest rate, compounded quarterly. Assuming that neither Grace nor Georgia makes any other deposits or withdrawals and that x, y, and z are positive numbers no greater than 50, whose savings account will contain more money at the end of exactly one year?
(1) z = 4
(2) 100y = zx
Your help is desperately needed folks please.
Responding to a pm:
Actually, u0422811's solution is perfect. That is exactly what went through my mind when I read this question.
Quarterly compounding yields more than annual compounding but the difference is minuscule in % terms.
e.g. if you invest $10 at 10% annual compounding, you get $11 at the end of the year.
but if you invest $10 at 10% quarterly compounding, you get $11.038 at the end of the year.
You get a small fraction of interest extra.
So x is invested at annual compounding and y at quarterly compounding. If x=y, the amount received from y will be a little more.
Statement 1 tells us z = 4. We need to compare x with y so this is not sufficient.
Statement 2 tells us 100y = zx
x/y = 100/z
Since maximum value of z is 50, x is at least twice of y.
If z% = 50%, amount obtained from x is 1.5x (= 3y) and that obtained from y is a little more than 1.5y.
Definitely an investment of $x results in a higher amount at the end of the year.
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