Question

The difference between the compound interest and the simple interest for 2 years at 8% per annum on a certain sum of money is 120. Find the sum​

Answer 1

Given :

The difference between the compound interest and the simple interest for 2 years at 8% per annum on a  certain sum of money is 120.

To find :

Sum of money

Solution :

We have :

CI - SI = 120

Time (n) = 2 years

Rate of interest (r) = 8% per annum

We know,

SI = Prn/100

CI = P(1 + r/100)ⁿ - P

​ Now atq,

⇒ [P(1 + r/100)ⁿ  - P] - Prn/100 = 120

⇒ [P(1 + 8/100)² - P] - (P * 8 * 2)/100 = 120

⇒ [P(1 + 0.08)² - P] - (16p/100) = 120

⇒ [P(1.08)² - P] - 0.16P = 120

⇒ [P * 1.1664 - P] - 0.16P = 120

⇒ [1.1664P - P] - 0.16P = 120

⇒ 0.1664P - 0.16P = 120

⇒ 1664P/10000 - 16P/100 = 120

⇒ (1664P - 1600P)/10000 = 120

⇒ 64P = 1200000

⇒ P = 1200000/64

⇒ P = 18750

Therefore,

Sum of money = Rs. 18750

Answer 2

Answer :-

Here the concept of Simple Interest and Compound interest has been used. According to this, the Simple Interest is the Principal × Rate × Time divided by 100 . Also, here we just have to apply the values, and find the sum. Let's do it.

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★ Formula Used :-

$\: \boxed{\boxed{\rm{Simple \: Interest \: = \: \dfrac{P \: \times \: R \: \times \: T}{100}}}}$

$\: \boxed{\boxed{\rm{Compound \: Interest \: = \: P \: \times \: (1 \: + \: \dfrac{R}{100})^t \: - \: P}}}$

where P is the principal, R is the rate, and T is the time.

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★ Solution :-

Given,

» Difference between SI and CI = 120

» Time Period = T = 2 years

» Rate = R = 8 %

Now according to the question :-

❐ CI - SI = 120

❐ P{1 + (R/100)}² - P - {(P × R × T)/100} = 120

❐ P{1 + (8/100)}² - P - {(P × 8 × 2) /100} = 120

❐ P(1 + 0.08)² - P - (16p/100) = 120

❐ P(1.08)² - P - 0.16P = 120

❐ P(1.1664) - P - 0.16P = 120

❐ 1.1664P - P - 0.16P = 120

❐ 0.1664P - 0.16P = 120

Multiplying all the terms by 10000. Then,

❐ 1664P - 1600P = 120

❐ 64P = 1200000

$\: \rm{\large{\longrightarrow \: \: P \: = \: \dfrac{1200000}{64}}}\: = \: 18750$

$\: \: \boxed{\boxed{\large{\sf{Sum \: = \: Rs. \: 18750}}}}$

$\: \boxed{\bf{\leadsto \: \: Hence, \: the \: sum \: is \: \boxed{Rs. \: 18750}}}$

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$\: \: \: \huge{\boxed{\tt{\large{More \: to \: know \: :-}}}}$

• Simple Interest is the interest compound yearly just using the normal method for a simple term.

• Compound Interest is the interest compounded yearly and monthly too but using compound technique and methods for a term.

• Time is the period for which interest is given.

• Rate is the percentage of interest given on the sum.