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
Answers
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
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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