Bunuel wrote:
Juliana has three options to invest her money for one year. Option A is discounted notes that she can buy for $98 and cash in for a face value of $100 a year later. Option B is a savings account that pays a 2% annual interest rate compounded semi-annually. Option C is an account that pays 2.03% simple interest for one year. Which of the answer choices represents the percent returns from the three choices in order from lowest to highest?
A) A, B, C
B) A, C, B
C) B, C, A
D) C, A, B
E) C, B, A
Let us start from option B, from interest rate theory we know the effective annual rate of 2% compounded twice is slightly higher than 2%.
\((1+\frac{0.02}{2})^2 = (1 + 0.01)^2 = 1 + 2*1*0.01 + 0.01^2 = 1.0201\), so the annual rate is \(2.01\%\).
Now we know B < C which leaves us with choices A or C.
Option A has an has an annual rate of \(\frac{100-98}{98} = 2/98 = 1/49 = \frac{100}{49}\% = (2 + \frac{2}{49})\%\), note 1/49 is about 2%, so \(2 + \frac{2}{49} \approx 2.04\) and the effective rate is \(2.04\%\). Finally we have B < C < A so we choose C.
Ans: C
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