What is the compound interest on 16000 for 9 months at 20% per annum interest compounded quarterly?

Find the compound interest on ₹ 16000 at the rate of 20% per annum for 6 months if the interest is compounded quarterly?

₹ 1640
₹ 1600
₹ 1680
₹ 1620

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Find the compound interest on ₹ 16000 at the rate of 20% per annum for 6 months if the interest is compounded quarterly?
Answer (Detailed Solution Below)
The compound interest on Rs 16000 for 9 months at 20% per annum, interest being compounded quarterly, is = ?
Solution(By Examveda Team)
Click here to read 1000+ Related Questions on Compound Interest(Arithmetic Ability)
What is the compound interest on Rs 16000 at 20% per annum for 9 months compounded quarterly 3 points Rs 2255 Rs 2500 Rs 2000 Rs 2522?
What is the compound interest on 20000 for 9 months at the rate of 4% per annum when interest is compounded quarterly?
What will be the compound interest of 16000?
How do you calculate 9 month CI?

Answer (Detailed Solution Below)

Option 1 : ₹ 1640

Given:

Principal = ₹ 16000

Rate = 20%

Time = 6 months = 1/2 year

Interest is compounded quarterly

Concept Used:

If interest is compounded quarterly means interest is calculated in every three months that is 4 times in a year.

We can simply convert this problem into a normal compound interest problem by multiplying the time by 4 and dividing the rate by 4

Formula Used:

Amount = Principal[1 + (Rate/100)]Time

Amount = Principal + Interest

Calculation:

New rate = 20%/4 = 5%

New time = 1/2 × 4 = 2 years

Amount = ₹ 16000[1 + 5/100]2

⇒ ₹ 16000[1 + 1/20]2

⇒ ₹ 16000[21/20]2

⇒ ₹ 16000[441/400]

So, Principal + Interest = ₹ 17640

⇒ Interest = ₹ 17640 – ₹ 16000

⇒ Interest = ₹ 1640

∴ The compound interest on ₹ 16000 at the rate of 20% per annum for 6 months if the interest is compounded quarterly is ₹ 1640

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

Aptitude
Simple and compound interest

A) Rs. 2,520

B) Rs. 2,524

C) Rs. 2,522

D) Rs. 2,518

Correct Answer:

Description for Correct answer:
Principal= Rs. 16000,

Rate %=20 %

Time= 9 months

When interest is being compounded quaterly

Time=$ \Large \frac{9}{12} \times 4=3 $

Rate =$ \Large \frac{20}{4} \%=5 \%=\frac{1}{20} $

According to the question,

8000 units = Rs. 16000

1 unit = Rs. 2

1261 units = Rs.$ \Large 2 \times 1261$

= Rs. 2522

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

The compound interest on Rs 16000 for 9 months at 20% per annum, interest being compounded quarterly, is = ?

A. Rs. 2520

B. Rs. 2524

C. Rs. 2522

D. Rs. 2518

Answer: Option C

Solution(By Examveda Team)

The interest is compounded quarterly,
$$\therefore R = \frac{{20}}{4} = 5\% $$
Time = 3 quarters
$$\eqalign{ & \therefore C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr & = 16000\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr & = 16000\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1} \right] \cr & = 16000\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr & = 16000 \times \frac{{1261}}{{8000}} \cr & = {\text{Rs}}{\text{.}}\,\,2522 \cr} $$

Q. The compound interest on 16000 Rs. for 9 months at 20% per annum, interest being compounded quarterly, is:
Answer: [C] Rs. 2522
Notes: The interest is compounded quarterly, $ \therefore R = \frac{20}{4} = 5\%$ Time = 3 quarters $ \therefore C.I. = P\left [ \left ( 1+\frac{R}{100} \right )^{T} – 1 \right ]$ $ = 16000\left [ \left ( 1+\frac{5}{100} \right )^{3} – 1 \right ]$ $ = 16000\left [ \left ( \frac{21}{20} \right )^{3} – 1 \right ]$ $ = 16000\left ( \frac{9261 – 8000}{8000} \right )$ $ = 16000\times \frac{1261}{8000} = 2522 Rs.$ Hence option [C] is correct answer.

The compound interest on a certain sum of money at 11% for 2 years is ₹6963. Its simple interest (in ₹) at the same rate and for the same period is:

A) ₹6750	B) ₹6600
C) ₹6000	D) ₹6500