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22 May 2020, 10:12
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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
02 Jun 2020, 03:29
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Bunuel
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%
A. 4.4%
B. 6.8%
C. 7.8%
D. 12.6%
E. 15.6%
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
24 May 2020, 03:19
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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.
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.
