Kevin deposited x hundred dollars in a bank that pays Y

BTGmoderatorLU wrote:Source: Economist GMAT

Kevin deposited x hundred dollars in a bank that pays Y percent annual interest, where Y is a single-digit positive integer, compounded semi-annually. How much money will Kevin have in his account after one year?

$$A.\ 100x\cdot\left(1+\frac{0.0Y}{2}\right)^2$$
$$B.\ x\cdot\left(1+Y\right)^2$$
$$C.\ 2\cdot\left(x+0.Y\right)^2$$
$$D.\ x\cdot\left(1+0.Y\right)^2$$
$$E.\ x\cdot\left(1+0.0Y\right)^2$$

The OA is A

Since the interest is compounded semi-annually, we have to consider the rate = Y/2 and period of compounding = 1*2 = 2 periods. The sum invested given = x hundred dollars = $ 100x

The formula for compounding is

A = P(1 + r/100)^n, where A = Amount, P = Principal = 100x, r = Rate of interest = Y/2 and n = Number of periods = 2

Thus, A = 100x[1 + (Y/2)/100]^2

A = 100x[1 + (Y/100)/2]^2

A = 100x[1 + 0.01*Y/2]^2

A = 100x[1 + 0.0*Y/2]^2. Note that it is given that Y is a single-digit integer, thus, 0.01*Y = 0.0Y

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Economist GMAT

Kevin deposited x hundred dollars in a bank that pays Y percent annual interest, where Y is a single-digit positive integer, compounded semi-annually. How much money will Kevin have in his account after one year?

$$A.\ 100x\cdot\left(1+\frac{0.0Y}{2}\right)^2$$
$$B.\ x\cdot\left(1+Y\right)^2$$
$$C.\ 2\cdot\left(x+0.Y\right)^2$$
$$D.\ x\cdot\left(1+0.Y\right)^2$$
$$E.\ x\cdot\left(1+0.0Y\right)^2$$

The OA is A

The compound interest formula is A = P(1 + r/t)^nt. For this question, P = 100x = the principal; r = 0.0Y = the interest rate (expressed as a decimal); t = 2 = the number of times per year that interest is compounded; and n = 1 = the number of years the money is in the bank.

Using the compound interest formula, in one year Kevin will have:

100x(1 + 0.0Y/2)^2

Answer: A