Question

A sum invested in compound interest (CI) at a certain rate for three years earns the same interest as it would
earn by way of an investment in simple interest (SI) at the rate of 18.2% for four years. How much more or
less is the percentage rate in case of the CI than that in the case of the SI?
O
551131160
1551131160_
1551131160
1551131160
20.63
O 18.43
1551131160
1551731160
155113116
1551131160 19
1551131160
15571311
1131160 10
1511311601
1551131160 19
16.950 19​

Answer 1

Answer:

ꜱɪᴍᴩʟᴇ ɪɴᴛᴇʀᴇꜱᴛ, ꜱ.ɪ. = ʀꜱ. 1260 = 100ᴩʀ×2 =  50ᴩʀ          -(ɪ)

ᴄᴏᴍᴩᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ, ᴄ.ɪ. = ᴀᴍᴏᴜɴᴛ(ᴀ) - ᴩʀɪɴᴄɪᴩʟᴇ(ᴩ)

=ᴩ(1+100ʀ)2 - ᴩ = ᴩʀ(ʀ/10000+1/50)=ʀꜱ.1323         -(ɪɪ)

ᴅɪᴠɪᴅɪɴɢ (ɪɪ) ʙy (ɪ),

200ʀ+1 = 12601323

⇒ʀᴀᴛᴇ,ʀ=10%ᴩ.ᴀ.

ɴᴏᴡ, 100ᴩʀᴛ=1260

⇒ 100ᴩ×10×2=1260

⇒ ᴩʀɪɴᴄɪᴩᴀʟ ᴏʀ ꜱᴜᴍ , ᴩ = ʀꜱ.6,300

Answer 2

Given :- A sum invested in compound interest (CI) at a certain rate for three years earns the same interest as it would earn by way of an investment in simple interest (SI) at the rate of 18.2% for four years. How much more or

less is the percentage rate in case of the CI than that in the case of the SI ?

Solution :-

Let the sum is P , and CI rate is R% per annum.

we know that,

• CI = P[{1 + (R/100)}^Time - 1]
• SI = (P * R * T)/100

given ,

• Time for CI = 3 years.
• Time for SI = 4 years .
• Rate for SI = 18.2 % .
• interest is same in both .

Putting all values we get,

→ P[{1 + (R/100)}³ - 1] = (P * 18.2 * 4)/100

P will be cancel from both sides,

→ {1 + (R/100)}³ - 1 = (728/1000)

→ {1 + (R/100)}³ = (728/1000) + 1

→ {1 + (R/100)}³ = (728 + 1000)/1000

→ {1 + (R/100)}³ = (1728/1000)

→ {1 + (R/100)}³ = (12/10)³

→ {1 + (R/100)}³ = {1 + (2/10)}³

→ {1 + (R/100)}³ = {1 + (20/100)}³

Comparing both sides now, we get,

→ R = 20% per annum .

Therefore,

→ Difference between rate = 20 - 18.2 = 1.8% (Ans.)

Hence, CI rate is 1.8% more than SI rate.

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