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​..
plz help.....​

Answer 1

Answer:

The sum of money is Rs. 18750

Answer 2

✠ ʟᴇᴛ ᴜs ғɪʀsᴛ ᴜɴᴅᴇʀsᴛᴀɴᴅ:–

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.

✠ ғᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :–

• SI = (P × R × T)/100
• CI = P × (1 + R/100)ᵗ – P

Where:—

• P = principal
• R = rate
• T = time

✠ ɢɪᴠᴇɴ:–

• 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

→ P = 1200000/64

→ P = 18750

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

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

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

• 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.