Question

The difference between simple and compound interest on a certain sum of money lent

for 3 years at 6 % p.a. is 137.70. Find the Principal.
​

Answer 1

Answer:

Let principle amount =x

Simple interest =

100

P×R×T

P=Principle=x

R=Rate=10% Per annum

T=Time =3 years

⇒S.I=

100

x×10×3

=

10

3x

Compound interest=Amount − Principle

Amount =P(1+

100

R

)

T

=x(1=

100

10

)

3

=x(

10

11

)

3

⇒C.I=

1000

1331x

−x

=

1000

1331x−1000x

=

1000

331x

Difference of C.I and S.I=93

⇒

1000

331x

−

10

3x

=93

⇒

1000

31x

=93

⇒x=

31

93×1000

=3000Rs.

⇒ Sum =3000Rs.

solution

Answer 2

Answer:

The principal amount is Rs 136.33

Step-by-step explanation:

Let the principal is P

Time given=t= 3yrs

Rate of interest=r=6%per annum

difference between Compound interest (CI) and simple interest (SI) =CI-SI= 137.70

SI is given by=

$\frac{prt}{100| }$

=

$\frac{p \times 6 \times 3}{100 } = \frac{18p}{100}$

CI is given by=

$p( {1 + \frac{r}{100} )}^{t}$

=

$p(1 + { \frac{6}{</strong><strong>100</strong><strong>}) }^{3}$

=

$p( { \frac{106}{100} )}^{3}$

=

$\frac{1191.01}{1000} p$

According to question

CI-SI=

$\frac{1191.01p}{1000} - \frac{18p}{100} = 137.70$

$\frac{1191.01p - 180p}{1000} = 137.70$

$1011p = 137.70 \times 1000$

$p = \frac{1000 \times 137.70 }{1011}$

p=Rs 136.33