The simple interest on a certain sum of money for 3 yrs is $225 and th

Question

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

GMATinsight · Accepted Answer

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

Archit3110 · Answer

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

Chethan92 · Answer

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.

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

Archit3110 · Answer

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

EgmatQuantExpert · Answer

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

Regards,

exc4libur · Answer

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).

bumpbot · Answer

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The simple interest on a certain sum of money for 3 yrs is $225 and th

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