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rheam25
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If an investment principal p decreased d percent in each of the first 09 Feb 2020, 12:14
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81% (01:27) correct 19% (01:19) wrong based on 269 sessions

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If an investment principal p decreased d percent in each of the first two years and recovered i percent in the third year, which of the following represents the value of the investment at the end of the third year?

A) p(1−d)(1+i)

B) \(p(1−d)^2\)(1+i)

C) p(1− \(\frac{d}{100}\) )(1+ \(\frac{i}{100}\) )

D) \(p(1−\frac{d}{100})^2\)(1+\( \frac{i}{100} \))

E) p(1−\( \frac{d}{10000} \))(1+ \(\frac{ i}{100 } \))
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D
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If an investment principal p decreased d percent in each of the first 09 Feb 2020, 12:23
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sujoykrdatta : could you please help me out with the explanation for this?
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If an investment principal p decreased d percent in each of the first 09 Feb 2020, 12:27
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If an investment principal p decreased d percent in each of the first two years and recovered i percent in the third year, which of the following represents the value of the investment at the end of the third year?

A) p(1−d)(1+i)

B)\(p(1−d)^2\)(1+i)

C)p(1− \(\frac{d}{100}\) )(1+ \(\frac{i}{100}\) )

D)\(p(1−\frac{d}{100})^2\)(1+\( \frac{i}{100} \))

E) p(1−\( \frac{d}{10000} \))(1+ \(\frac{ i}{100 } \))
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Answer D

1st year
\(P*(1-\frac{d}{100})\)

2nd year
\(P*(1-\frac{d}{100})-P(1-\frac{d}{100})*\frac{d}{100 }\)-> \(P(1-\frac{d}{100})(1-\frac{d}{100})\)

3rd year
\(P(1-\frac{d}{100})(1-\frac{d}{100})+P(1-\frac{d}{100})(1-\frac{d}{100})*\frac{i}{100}\) -> \(P(1-\frac{d}{100})^2(1+\frac{i}{100})\)
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If an investment principal p decreased d percent in each of the first 09 Feb 2020, 12:31
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rheam25
If an investment principal p decreased d percent in each of the first two years and recovered i percent in the third year, which of the following represents the value of the investment at the end of the third year?

A) p(1−d)(1+i)

B)\(p(1−d)^2\)(1+i)

C)p(1− \(\frac{d}{100}\) )(1+ \(\frac{i}{100}\) )

D)\(p(1−\frac{d}{100})^2\)(1+\( \frac{i}{100} \))

E) p(1−\( \frac{d}{10000} \))(1+ \(\frac{ i}{100 } \))

Answer D

1st year
\(P*(1-\frac{d}{100})\)

2nd year
\(P*(1-\frac{d}{100})-P(1-\frac{d}{100})*\frac{d}{100 }\)-> \(P(1-\frac{d}{100})(1-\frac{d}{100})\)

3rd year
\(P(1-\frac{d}{100})(1-\frac{d}{100})+P(1-\frac{d}{100})(1-\frac{d}{100})*\frac{i}{100}\) -> \(P(1-\frac{d}{100})^2(1+\frac{i}{100})\)
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In the second year why are we multiplying \(P(1- \frac{d}{100}) with \frac{d}{100}\)
Could you please explain the 2nd year working in detail? I'm a bit lost :think:
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If an investment principal p decreased d percent in each of the first 09 Feb 2020, 12:34
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shameekv1989
rheam25
If an investment principal p decreased d percent in each of the first two years and recovered i percent in the third year, which of the following represents the value of the investment at the end of the third year?

A) p(1−d)(1+i)

B)\(p(1−d)^2\)(1+i)

C)p(1− \(\frac{d}{100}\) )(1+ \(\frac{i}{100}\) )

D)\(p(1−\frac{d}{100})^2\)(1+\( \frac{i}{100} \))

E) p(1−\( \frac{d}{10000} \))(1+ \(\frac{ i}{100 } \))

Answer D

1st year
\(P*(1-\frac{d}{100})\)

2nd year
\(P*(1-\frac{d}{100})-P(1-\frac{d}{100})*\frac{d}{100 }\)-> \(P(1-\frac{d}{100})(1-\frac{d}{100})\)

3rd year
\(P(1-\frac{d}{100})(1-\frac{d}{100})+P(1-\frac{d}{100})(1-\frac{d}{100})*\frac{i}{100}\) -> \(P(1-\frac{d}{100})^2(1+\frac{i}{100})\)

In the second year why are we multiplying \(P(1- \frac{d}{100}) with \frac{d}{100}\)
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Because the new value in 2nd year will be the principal from 1st year which is \(P*(1-\frac{d}{100})\) and this value will be decreased by d percent in 2nd year.
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If an investment principal p decreased d percent in each of the first 09 Feb 2020, 12:53
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sujoykrdatta : could you please help me out with the explanation for this?
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Question:
If an investment principal \(p\) decreased \(d\) percent in each of the first two years and recovered \(i\) percent in the third year, which of the following represents the value of the investment at the end of the third year?

Initial value = \(p\)
After 1 year, the value decreased by \(d\)%; thus, the value becomes \((100 - d)\)% of the initial value

=> \(V1\) (value after 1 year) = \((100-d)\)% of \(p\)

After 1 more year, the value decreased by \(d\)%; thus, the value becomes \((100 - d)\)% of the value \(V1\)

=> \(V2\) (value after 2 years) = \((100-d)\)% of \((100-d)\)% of \(p\)


After 1 more year, the value increased by \(i\)%; thus, the value becomes \((100 + i)\)% of the value \(V2\)

=> \(V3\) (value after 3 years) = \((100+i)\)% of \((100-d)\)% of \((100-d)\)% of \(p\)

\(= [(100+i)/100] * [(100-d)/100] * [(100-d)/100] * p\)

\(= [1+(i/100)] * [1-(d/100)] * [(1-(d/100)] * p\)

\(= p*[1-(d/100)]^2 * [1+(i/100)]\)

Answer D


Hope this helped :thumbup:
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If an investment principal p decreased d percent in each of the first 25 Sep 2024, 22:37
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