Question

Find the different between the compound interest and simple interest on a sum of $64000 for 2 year at the 7,one and half% pa. ​

Answer 1

Given :-

The Principal = $ 64000

Time = 2 years

Rate of interest = 7%

To find :-

The difference between the Compound Interest and Simple Interest.

Solution :-

Given that

★ Principal (P) = $ 64000

★ Time (T) = 2 years

★ Rate of Interest (R) = 7%

♦ Compound interest :-

If the interest is calculated per annum compoundly then the number of time for 2 years the interest is calculated = (n) = 2

We know that

■ Amount = P[1+(R/100)]^n

=> A = 64000[1+(7/100)]²

=> A = 64000[(100+7)1/100]²

=> A = 64000[(107/100)²]

=> A = 64000×107×107/10000

=> A = 64×107×107/10

=> A = 732736/10

=> A = 73273.6

The Amount after 2 years = $ 73273.6

We know that

■ Amount = Principal + Interest

=> Interest = Amount - Principal

=> Interest = 73273.6 - 64000

=> Interest = 9273.6

The Compound Interest = $ 9273.6

♦ Simple interest :-

We know that

■ Simple interest = PTR/100

=> Simple Interest = (64000×2×7)/100

=> Simple Interest = 640×2×7

=> Simple Interest = 8960

The Simple Interest = $ 8960

Now,

The difference between the CI and SI

= 9273.6 - 8960

= 313.6

The Difference = $ 313.6

Alternative Method :-

■ The difference between the CI and SI is D for 2 years then D = P(R/100)²

Now,

D = 64000(7/100)²

=> D = 64000×(7×7)/(100×100)

=> D = 64000×49/10000

=> D = 64×49/10

=> D = 3136/10

=> D = 313.6

The difference = $ 313.6

Answer :-

★ The difference between the Compound Interest and Simple Interest is $ 313.6

Used formulae:-

→ Amount = P[1+(R/100)]^n

→ Simple interest = PTR/100

→ The difference between the CI and SI is D for 2 years then D = P(R/100)²

• P = Principal
• T = Time
• R = Rate of Interest
• n = Number of times the interest is calculated compoundly.

Answer 2

$\huge\red{A}\pink{N}\orange{S} \green{W}\blue{E}\gray{R} =$

Given:

The Principal -564000

Time = 2 years

Rate of interest=7%

To find :

The difference between the Compound

Interest end Simple Interest

Solution :

Given that

* Principal (P) = $ 64000

* Time (T) = 2 years

* Rate of Interest (R) -7%

• Compound interest :

If the interest is calculated per annum

compoundly then the number of time for

2 years the interest is calculated=(n)=2

We know the!

Amount P[1+(R/100))

⇒ A=64000(1+(7/1001|²

A-640000100+70/0001

A=64000107/1001

⇒ A=54000-107-107/10000

A 64-107-107/10

⇒ A=732736/10

⇒ A=732738

The Amount ofter 2 years $73273.6

We know that

Amount Principal + Interest

Interest Amount-Principal

= Interest=73273.6-64000

Interest -9273,6

The Compound Interest-$9273.6

*Simple interest

We know that

Simple interest=PTR/100

Simple Interest -(64000-2-7700

Simple Interest=640-2x7

Simple Interest -9960

The Simple Interest - $ 8960

Now,

The difference between the Cl and Sl

-9273.6-8060

*313.6

The Difference $313.6

Alternative Method >>

The difference between the Cl and Si

is D for 2 years then D=P(R/100)

Now,

D=54000/7/1001

⇒ B=64000 17x7y100×100)

D=64000-49/10000

D-64-49/10

0=3136/10

The difference - $ 313.6

Answer:

* The difference between the

Compound Interest and Simple Interest

in $313.6

Used formulae:

-Amount=P[1+(R/100

- Simple Interest=PTR/100

*The difference between the Cl and Si

is D for 2 years then D-PR/100)

P-Principal

- T-Time

-R-Rate of Interest

*n* Number of times the interest is

calculated compoundly.