Find the compound interest on ₹ 20000 at 10% per annum for 2 years 3 months compounded annually

Correct Answer:

Description for Correct answer:
The amount at the end of “n" years of Investing in compound interest,

\( \Large A=P \left(1+\frac{r}{100}\right)^{n} \)

Here, the Principal P = 20,000, number of years n = 2, rate of interest r = 20%.

Therefore, Amount \( \Large A=20000 \left(1+\frac{20}{100}\right)^{2}=20000 \left(\frac{36}{25}\right) \) = Rs.28,800.

Compound Interest C.I. = Amount - Principal = 28,800 - 20,000 = Rs.8,800.

Part of solved Simple and compound interest questions and answers : >> Aptitude >> Simple and compound interest

Find the compound interest on Rs. 20000 at 20 percent per annum for 12 months, compounded half yearly. 

1. Rs. 4000 
2. Rs. 4500
3. Rs. 4200
4. Rs. 4400 

Answer (Detailed Solution Below)

Option 3 : Rs. 4200

Free

CT 1: Growth and Development - 1

10 Questions 10 Marks 10 Mins

Given:

Principal = Rs. 20000,

Rate = 10 % per half-year,

Time = 1 years = 2 half- years

Formula:

Amount = P (1 + (R/2)/100)2n 

Calculations:

Amount = 20000 [1 + 10/100]2

Amount = Rs. 24,200

Compound Interest = Total amount – Principal

⇒ 24,200 – 20000

⇒ Rs.4200

∴ The required answer is Rs 4200.

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

Find the compound interest (in Rs.) on Rs. 20000 in 2 years if the rate of interest is 4% per annum for the first year and 8% per annum for the second year.

1. 2464
2. 2130
3. 2500
4. 2375

Answer (Detailed Solution Below)

Option 1 : 2464

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CT 1: International and National Awards

10 Questions 10 Marks 8 Mins

GIVEN:

Principal = Rs. 20000

Rate = 4%

CONCEPT:

Compound interest concept.

The amount after 1 year will be principal for 2nd year.

FORMULA USED:

For CI:

A = P(1 + R/100)T

A = P + CI

Where P is principal, R is rate of interest and T is time.

CALCULATION:

After first year the amount = \(20000 \times \left( {1 + \frac{4}{{100}}} \right) = 20000 \times \left( {\frac{{104}}{{100}}} \right)\)

After second year the amount = \(20000 \times \left( {\frac{{104}}{{100}}} \right) \times \left( {\frac{{108}}{{100}}} \right)\)

= \(20000 \times \left( {\frac{{26}}{{25}}} \right) \times \left( {\frac{{27}}{{25}}} \right)\)

= Rs. 22464

CI = A - P

⇒ CI = 22464 –  20000

⇒ Rs. 2464

∴ The compound interest for 2 years is Rs. 2464.

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

Find the compound interest on Rs. 20,000 at 10% per annum for 3 years.

Answer

Verified

Hint:- We had to only apply compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] directly to get the amount after 3 years and then subtract initial amount to get the compound interest for 3 years.Complete step-by-step solution -
As we know that the principal amount is Rs. 20,000.
Rate of interest is 10% at annual rate.
And the rate of interest is compounded annually.
So, now we can apply compound interest formulas to find the amount after three years.
According to compound interest formula compound interest for t years is calculated as \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\]where r is the annual rate of interest, t will be number of years after which we had to find the amount, P will be the principal amount and A will be the amount after t years.
So, according to the question,
P = Rs. 20,000
r = 10%
and t = 3 years.
So, putting all the values in the formula of compound interest we will get,
\[A = 20000{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} = 20000{\left( {\dfrac{{110}}{{100}}} \right)^3}\]
So, \[A = 20000 \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} = \dfrac{{2 \times 110 \times 110 \times 110}}{{100}} = 26620\]
So, the amount after three years will be equal to Rs. 26,620.
Now the compound interest for three years will be = Amount after three years – Initial amount.
So, the compound interest for 3 years will be = Rs. 26,620 – Rs. 20,000 = Rs. 6,620
Hence, the compound interest for three years will be Rs. 6,620.

Note:- Whenever we come up with this type of question, we should note that simple interest and compound interest are not the same because simple interest is based on the principal amount of a loan or deposit. But in contrast, compound interest is based on the principal amount and the interest that accumulates on it every period. So, we had to put values in the compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] (where A is the amount invested, r is the rate of interest annually and t will be the total number of years) to get the amount after three years (A).