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Math Expert
Joined: 02 Sep 2009
Posts: 52905
The simple interest on a certain sum of money for 3 yrs is $225 and th [#permalink] ### Show Tags 29 Jan 2019, 00:58 00:00 Difficulty: (N/A) Question Stats: 25% (01:43) correct 75% (03:03) wrong based on 7 sessions ### HideShow timer Statistics 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

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The simple interest on a certain sum of money for 3 yrs is $225 and th [#permalink] ### Show Tags Updated on: 30 Jan 2019, 03:06 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
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Originally posted by Archit3110 on 29 Jan 2019, 01:18.
Last edited by Archit3110 on 30 Jan 2019, 03:06, edited 2 times in total.
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The simple interest on a certain sum of money for 3 yrs is $225 and th [#permalink] ### Show Tags 29 Jan 2019, 01:54 As simple interest is the same for each year. SI per year = 225/3 = 75$.
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

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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, 02:26 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 _________________ | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com SVP Joined: 18 Aug 2017 Posts: 1770 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: The simple interest on a certain sum of money for 3 yrs is$225 and th  [#permalink]

### Show Tags

29 Jan 2019, 02:32
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

EgmatQuantExpert
could you please explain the highlighted part , how did you get that? why is CI subtracted with P?
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### Show Tags

29 Jan 2019, 02:53
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

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