Total Money invested = $91.25 * 100 bonds = $9125
Money received after two years = $100 * 100 bonds + 2.75% of 100 for 100 bonds for 2 years = 100 * 100 + (2.75/100) *100 *100*2
= 10000 + 550 = 10550

Total Profit = $10550 - $9125 = $1425

$1425 is effective return on the $9125 investment after two years
or we can say that $1425 is the interest earned when $9125 is invested at r% annually
Using SI= PRT/100
1425 = (9125 * r * 2)/100

r=7.80 or 7.8% (rounded to nearest tenth decimal)

C.
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The cost price of getting 100 bonds for 91.25$ is 9125$

She collected the par value in 2 year period.
100*100=10,000$
Also. She got 2.75$ premium per bond/annum.
100*2.75*2 (for two years)=550

Total amount she received is 10000+550=10550

The ROI percent she have is Revenue-Cost/Cost*100
(10550-9125)*100/9125
142500/9125
15.6 (approximate) for two years.
Per annum ROI will be 15.6/2=7.8
Since in simple interest, interest amount never changes over the period of time.
Answer is C

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For each bond:
Ms. Kessler paid $91.25 but collected after 2 years $100.
Since the amount earned over 2 years = 100-91.25 = 8.75, the amount earned each year = \(\frac{8.75}{2} ≈ $4.37\)
Additional annual interest = 2.75% of the $100 par value = $2.75
Total return = 4.37 + 2.75 = $7.12

Thus:
Simple annual interest for each $91.25 bond \(= \frac{7.12}{91.25} * 100 ≈ \frac{7}{90} * 100 = \frac{70}{9} =\) a bit less than 8


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Bunuel
How can we assume that the statement " In addition she collected interest for the 2 years at an annual rate of 2.75 percent of par value" talks about simple interest and not compound interest? I got lost in calculating Compound interest!
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\(100 * $91.25 = $9,125\)
100 bonds at maturity \(= $10,000\)
2.75% par value \(= $275 * 2 = $550\)

\(10,000 + $550 = 10,550\)
\($10,550 - 9,125 = $ 1,425\)

\(\frac{1,425}{2} = 712.50\)

\(\frac{712}{9125} = 7.8\)%

Answer is C.
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Bunuel - can you please help me understand how to formulate the equation for "What was Ms. Kessler's effective simple annual interest rate of return on her investment". I thought it will be Total Interest earned (550) / Total cost (9125) * 100. Where did I go wrong?
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yashikaaggarwal Bunuel any suggestions on how to do this division quickly? I got stucked there
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We can roundoff digits to near hundreds to get answer easily, without indulging in more decimals.
Let's Quote 9125 as 9000 and 142500 as 142000
dividing 142000 with 9000 = 15.77
which is ROI for 2 years
1 year ROI will be 7.8 something
which is nearby option C

Hope this helps

Interest is always calculated as simple interest unless stated otherwise, so you have to calculate Simple interest here as no compound interest is mentioned.

ROI is calculated upon total earnings-cost, not just interest.
Ms. Kessler not only gained interest but the par value sale of the bonds which she purchased for less value.
so {(salevalue + Interest - purchase value)/purchase value}*100

Solution:

In total, each bond has a value of 100 + 100 x 0.0275 x 2 = $105.50 at the end of the 2 years. This is 105.5 - 91.25 = $14.25 more than its value at the beginning of the 2-year period. Since the extra $14.25 is for a 2-year period, the annual simple interest rate is:

(14.25/2) / 91.25 x 100 ≈ 7.8 percent

Answer: C
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ScottTargetTestPrep

Why are we multiplying 2 with 2.75 when it is not given in the question that this interest was per annum? How are we assuming that this percent interest was per annum?

Kindly please clear this doubt.

Gagan