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29 Jan 2019, 01:58
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The simple interest on a certain sum of money for 3 yrs is $225 and the compound interest on the same sum at the same rate for 2yrs is$153. What is the principal invested?

A. $1500 B.$1875

C. $2250 D.$2500

E. $2750 _________________ GMAT Club Legend Joined: 18 Aug 2017 Posts: 5706 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) The simple interest on a certain sum of money for 3 yrs is$225 and th  [#permalink]

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Updated on: 30 Jan 2019, 04:06
2
Bunuel wrote:
The simple interest on a certain sum of money for 3 yrs is $225 and the compound interest on the same sum at the same rate for 2yrs is$153. What is the principal invested?

A. $1500 B.$1875

C. $2250 D.$2500

E. $2750 SI=p*r*t/100 225=p*r*3/100 r/100= 75/p CI= P * ( 1+r/100) ^t Compounded amount in 2 years = P(1+r100)2P(1+r100)2 interest earned = Compounded amount in 2 years - Invested amount = P(1+r100)^2 - P 153=P*(1+r/100)^2-P 153=P*(1+75/P)^2-P solve for P 3P=75*75 p= 75*25 p= 1875 IMOB Originally posted by Archit3110 on 29 Jan 2019, 02:18. Last edited by Archit3110 on 30 Jan 2019, 04:06, edited 2 times in total. NUS School Moderator Joined: 18 Jul 2018 Posts: 1050 Location: India Concentration: Finance, Marketing GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities) The simple interest on a certain sum of money for 3 yrs is$225 and th  [#permalink]

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29 Jan 2019, 02:54
As simple interest is the same for each year. SI per year = 225/3 = 75$. SI = PTR/100 225 = PR*3/100 PR = 7500 Also, $$CI_2-SI_2 = \frac{PR^2}{100^2}$$ = 153-150 = 7500*R/10000 $$CI_2$$ and $$SI_2$$ are compound and simple interest for 2 years. R = 4% 75 = P*4*1/100 P = 1875 B is the answer. e-GMAT Representative Joined: 04 Jan 2015 Posts: 3219 Re: The simple interest on a certain sum of money for 3 yrs is$225 and th  [#permalink]

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29 Jan 2019, 03:26
1
2

Solution

Given:
• The simple interest on a certain sum of money for 3 years = $225 • The compound interest on the same sum at the same rate for 2 years =$153

To find:
• The principal amount invested

Approach and Working:
Let the principal amount invested = $P • Simple interest earned for 3 years =$$P * 3 * \frac{r}{100} = 225$$ o Implies, $$\frac{r}{100}= \frac{75}{P}$$ • Compound interest earned for 2 years = P(1 + r/100)^2 – P =$153
o Implies, $$P(1 + \frac{75}{P})^2 – P = 153$$
o $$(P + 75)^2 – P^2 = 153P$$
o $$150P + 75^2 = 153P$$
o $$3P = 75^2$$
• Therefore, P = 25 * 75 = 1875

Hence, the correct answer is Option B

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Re: The simple interest on a certain sum of money for 3 yrs is $225 and th [#permalink] Show Tags 29 Jan 2019, 03:32 EgmatQuantExpert wrote: Solution Given: • The simple interest on a certain sum of money for 3 years =$225
• The compound interest on the same sum at the same rate for 2 years = $153 To find: • The principal amount invested Approach and Working: Let the principal amount invested =$P
• Simple interest earned for 3 years =$$P * 3 * \frac{r}{100} = 225$$
o Implies, $$\frac{r}{100}= \frac{75}{P}$$

• Compound interest earned for 2 years = P(1 + r/100)^2 – P = $153 o Implies, $$P(1 + \frac{75}{P})^2 – P = 153$$ o $$(P + 75)^2 – P^2 = 153P$$ o $$150P + 75^2 = 153P$$ o $$3P = 75^2$$ • Therefore, P = 25 * 75 = 1875 Hence, the correct answer is Option B Answer: B EgmatQuantExpert could you please explain the highlighted part , how did you get that? why is CI subtracted with P? e-GMAT Representative Joined: 04 Jan 2015 Posts: 3219 Re: The simple interest on a certain sum of money for 3 yrs is$225 and th  [#permalink]

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29 Jan 2019, 03:37
1
Archit3110 wrote:
EgmatQuantExpert
could you please explain the highlighted part , how did you get that? why is CI subtracted with P?

Hi Archit3110,

Compounded amount in 2 years = $$P(1 + \frac{r}{100})^2$$

Now, the interest earned = Compounded amount in 2 years - Invested amount = $$P(1 + \frac{r}{100})^2$$ - P

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The simple interest on a certain sum of money for 3 yrs is $225 and th [#permalink] Show Tags 29 Jan 2019, 03:53 2 1 Bunuel wrote: The simple interest on a certain sum of money for 3 yrs is$225 and the compound interest on the same sum at the same rate for 2yrs is $153. What is the principal invested? A.$1500

B. $1875 C.$2250

D. $2500 E.$2750

Simple interest for 3 yrs is $225 i.e. Simple Interest for 1 year = 225/3 =$75 (Simple interest on a fixed sum remains same every year as the principle sum remains static)

i.e. Compound interest for first year = 75 (For first compounding Simple interest and compound interests are same... they start differing from second compounding)
Compound interest for Second year = 153 - 75 = 78

i.e. Coumpound interest for second year is 78-75 = $3 more which is interest charged on interest earned in previous compounding i.e. Interest earned on$75 = $3 i.e. interest rate = (3/75)*100 = 4% i.e. interest at Principle P for 1 year @4% =$75

i.e. (4/100)*P = 75

i.e. P = $1875 Answer: Option B _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html Click here for Our QUANT & VERBAL private tutoring package details ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION VP Joined: 24 Nov 2016 Posts: 1086 Location: United States Re: The simple interest on a certain sum of money for 3 yrs is$225 and th  [#permalink]

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07 Aug 2019, 13:11
Bunuel wrote:
The simple interest on a certain sum of money for 3 yrs is $225 and the compound interest on the same sum at the same rate for 2yrs is$153. What is the principal invested?

A. $1500 B.$1875
C. $2250 D.$2500
E. $2750 simple interest: principal • rate • years - principal = interest compound interest: principal • (1+rate)^years - principal = interest given: p(1+r/100)(3)-p=225 and p(1+r/100)^2-p=153; isolate (r/100): p(1+r/100)(3)-p=225 is the same as p(r/100)(3)=225,…(r/100)=(75/p) substitue (r/100): p(1+r/100)^2-p=153,… p(1+(75/p))^2-p=153,…p=1875 Answer (B). Re: The simple interest on a certain sum of money for 3 yrs is$225 and th   [#permalink] 07 Aug 2019, 13:11
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