Ms. Kessler bought 100 bonds for $91.25 each. At the end of 2 years th

Question

Ms. Kessler bought 100 bonds for $91.25 each. At the end of 2 years the bonds matured and she collected the par value of $100 each. In addition she collected interest for the 2 years at an annual rate of 2.75 percent of par value. What was Ms. Kessler's effective simple annual interest rate of return on her investment, to the nearest tenth of a percent?

A. 4.4%
B. 6.8%
C. 7.8%
D. 12.6%
E. 15.6%

PS20368

A. 4.4%
B. 6.8%
C. 7.8%
D. 12.6%
E. 15.6%

PS20368

GMATGuruNY · Accepted Answer

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

C

NitishJain · Answer

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.

yashikaaggarwal · Answer

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

Posted from my mobile device

jayarora · Answer

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!

Basshead · Answer

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.

A2208 · Answer

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?

Michele4 · Answer

yashikaaggarwal   Bunuel  any suggestions on how to do this division quickly? I got stucked there

yashikaaggarwal · Answer

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

yashikaaggarwal · Answer

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

yashikaaggarwal · Answer

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

ScottTargetTestPrep · Answer

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

gagan0303 · Answer

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

ScottTargetTestPrep · Answer

Response: 
The question says “In addition she collected interest for the 2 years at an annual rate of 2.75 percent of par value.”

GmatPoint · Answer

Interest earned per bond because of maturity = $100 - $91.25 = $8.75
Since this is the interest earned over a period of two years, 
Interest earned per bond each year for maturity = $8.75/2 = $4.375

Also, she collected interest at an annual rate of 2.75 of par value which is equal to $100*2.75/100 = $2.75

Thus, the total interest per bond per year = $4.375 + $2.75 = $7.125
Now, the principal amount invested per bond was $91.25.

Thus, effective interest rate = (7.125/91.25)*100 = 7.8%
Thus, the correct answer is C.

DanTheGMATMan · Answer

Just count the total earned per bond over 2 years, cut that in half for the per year earn, and put that over the original cost of the bond to her:

https://www.youtube.com/watch?v=DjOuz8bxM0A

Gemmie · Answer

Cost: 91.25 * 100 = 9125

Profit = (100 - 91.25) * 100 + 100 * 2.75 * 2 
        = 875 + 550 = 1425

RoR (of 2 years) =  \frac{1425}{9125} \approx{\frac{14}{91}} = 0.15

Simple annual RoR =  \frac{0.15}{2} = 0.075  
=> 7.8%

bumpbot · Answer

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Ms. Kessler bought 100 bonds for $91.25 each. At the end of 2 years th

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