What sum of money will amount to rs9261 in 3 years at 5% pa compound interest

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.

1. 12%
2. 11%
3. 5%
4. 10%
5. 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?

1. Rs. 2,500
2. Rs. 2,480
3. Rs. 2,560
4. 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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Book: Other Questions - Mathematics

Chapter: 8. Comparing Quantities

Subject: Maths - Class 8th

Q. No. 27 of Exercise

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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

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