At what rate will a sum of 3200 produce an interest of 672 in 2 years if compounded anually?

The sum of Rs. 3200 invested at 10% per annum compounded quarterly amounts to Rs. 3362, then find the time period.

1. ½ year
2. ¼ year
3. ¾ year
4. 1 year

Answer (Detailed Solution Below)

Option 1 : ½ year

Free

RRB Group D: Memory Based Question Full Test based on 17 Aug 2022

100 Questions 100 Marks 90 Mins

Given:

Principal = Rs 3200

Rate of interest = 10% per annum

Amount = Rs 3362

Concept used:

Amount = P × [1 + (r/100)]t

But here, the amount is calculated quarterly. Then the amount obtained will be:

Amount = P × [1 + r/(n × 100)]nt

Where n is the number of terms, here n = 4.

Calculation:

3362 = 3200 × [1 + 10/(4 × 100]4t

⇒ 3362/3200 = (41/40)4t

⇒ 1681/1600 = (41/40)4t 

⇒ (41/40)2 = (41/40)4t

On comparing powers,

⇒ 2 = 4t 

⇒ t = 1/2 

∴ The time period is 1/2 year.

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Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

What will be the difference between the compound interest (interest is compounded annually) and simple interest on a sum of Rs. 3200 at the rate of 20% per annum for 2 years?

1. Rs. 128
2. Rs. 148
3. Rs. 132
4. Rs. 96

Answer (Detailed Solution Below)

Option 1 : Rs. 128

Free

10 Questions 10 Marks 7 Mins

Given:

Principal = Rs. 3200

Rate of interest = 20%

Time = 2 years

Formula Used:

Simple interest = (principal × time × rate) / 100

Successive increase = {a + b + (a × b) / 100}

Calculation:

Simple Interest = (3200 × 20 × 2) / 100

⇒ Simple interest = Rs. 1280

Now,

Compound interest

Rate% = 20%

Time = 2

So {20 + 20 + (20× 20) / 100}

 ⇒ 44%

⇒Compound interest = 44% of 3200

⇒ Rs. 1408

∴ Difference between compound interest and simple interest = 1408 – 1280 = Rs. 128

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Let's discuss the concepts related to Interest and Simple and Compound Both. Explore more from Quantitative Aptitude here. Learn now!

At what rate will a sum of 3200 produce an interest of 672 in 2 years if compounded anually?

At what rate of interest will Rs 3200 amount to Rs 5000 in 2 years?

At what rate of compound interest a sum amount to Rs 672 in 2 years and to Rs 714 in 3 years when the interest is payable annually?

At what rate percent per annum compounded annually rupees 3200 will amount to rupees 3528 in 2 years?