A sum of money lent on compound interest amounts in 2 year to Rs. 8820 and in 3 years to Rs. 9261. Find the rate percent.
- 12%
- 11%
- 5%
- 10%
- None of these
Answer (Detailed Solution Below)
Option 3 : 5%
Given
Amount in 2 years = Rs 8820
Amount in 3 years = Rs 9261
Formula Used
A = P (1 + r/100)t
Calculation
A = P (1 + r/100)t
⇒ 8820 = P(1 + r/100)2 ……………………….(1)
⇒9261 = P(1 + r/100)3 ……………………..(2)
Divide (2) by (1), we have,
⇒ 9261/8820 = (1 + r/100)3/ (1 + r/100)2
⇒ 9261/8820 = 1 + r/100
⇒ (9261/8820) - 1 = r/100
⇒ 441/8820 = r/100
⇒ r = 5%
∴ The rate is 5%.
Concept used:
Amount on 3rd year - Amount on 2nd year = interest payble for 1 year on the 2nd year amount.
Hence,
9261 - 8820 = 8820 × r × 1 / 100
⇒ r = 44100/8820 = 5
∴ Rate of interest = 5%
We are calculating interest for 1 year, so we can use SI instead of CI.
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A sum of Rs. 8,000 invested at 10% p.a. amounts to Rs. 9,261 in a certain time, interest compounded half–yearly. What will be the compound interest (in Rs) on the same sum for the same time at double the earlier rate of interest, when interest is compounded annually?
- Rs. 2,500
- Rs. 2,480
- Rs. 2,560
- Rs. 2,520
Answer (Detailed Solution Below)
Option 3 : Rs. 2,560
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Given:
P = 8000, A = 9261 and r = 10%
If interest compounded half–yearly, then = 10/2 = 5%
As we know,
A = P (1 + r/100)t
⇒ 9261 = 8000 (1 + 5/100)t
⇒ (1 + 1/20 )t = 9261/8000
⇒ (21/20)t = (21/20)3
⇒ t = 3 years
As given, interest compounded half–yearly, then
Time = 3/2 years [1 year and 6 month]
Now,
P = 8000, r = 10 × 2 = 20% and t = 3/2
As we know,
A = P (1 + r/100)t
A = 8000 (1 + 20/100) × (1 + 10/100)
⇒ A = 8000 × 120/100 × 110/100
⇒ A = 10560
CI = 10560 – 8000 = 2560
As we know,
P : A for 1 year = ∛8000 : ∛9261 = 20 : 21
Percentage = 1/20 × 100 = 5% (satisfied)
Time = 1 year 6 month
Now, rate = 20%
Rate for 1 year 6 month = 20 + 10 + (20 × 10)/100 = 30 + 2 = 32%
⇒ 32% of 8000
⇒ 2560
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Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!
Book: Other Questions - Mathematics
Chapter: 8. Comparing Quantities
Subject: Maths - Class 8th
Q. No. 27 of ExerciseListen NCERT Audio Books to boost your productivity and retention power by 2X.
27
What sum of money will amount to Rs 9261 in 3 years at 5% per annum compound interest?
Given,
A = 9261
R = 5%
n = 3
So, we apply directly formula which is,
P = Rs. 8000