Find the amount and compound interest on 10,000 for 1 year at 12 per annum compounded half yearly

What is the compound interest on a sum Rs. 10,000 at 12% per annum for 1 year and 4 months, when the interest is compounded at every 8 months?

1. Rs. 1,364
2. Rs. 1,664
3. Rs. 1,504
4. Rs. 1,264

Answer (Detailed Solution Below)

Option 2 : Rs. 1,664

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SSC GD Previous Paper 2 (Held On: 13 Feb 2019 Shift 1)_Hindi

100 Questions 100 Marks 90 Mins

Given:

Principal = Rs. 10,000

Rate of interest = 12%

Time = 1 year and 4 months = 16 months

Formula used:

A = P (1 + r/100)n

C.I = A - P

Where, A = Amount, P = Principal, n = Time, C.I = Compound interest

Calculation:

Interest is compounded on 8 months,

So, Time = 16/8 = 2 years

Rate of interest = 12% × (8/12)  = 8%

A = P (1 + r/100)n

⇒ Amount = 10,000 × (1 + 8/100)2

⇒ Amount = 10,000 × (108/100)2

⇒ Amount = (108)2

⇒ Amount = Rs. 11,664

C.I = A - P

⇒ C.I = 11,664 – 10,000

⇒ C.I = 1,664

∴ The compound interest is Rs. 1,664.

Alternate Method

Interest is compounded on every 8 months

So, Time = 16/8 = 2 years

Rate of interest = 12% × (8/12)  = 8% 

Effective rate formula for two years = (A + B + AB/100)

Here, A = B = 8%

⇒ Effective rate formula for two years = {8 + 8 + (64/100)} = 16.64%

⇒ Compound interest = 10,000 × 16.64%

⇒ Compound interest = Rs. 1664

∴ The compound interest is Rs. 1,664.

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

Solution:

Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10% = 5% (compounded half yearly)

Time(n) = 1\ \frac{1}{2} years = 3 years (compounded half yearly)

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

= 10000\left(1+\frac{5}{100}\right)^3

= 10000\left(1+\frac{1}{20}\right)^3

= 10000\left(\frac{21}{20}\right)^3

= 10000\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}

= Rs. 11,576.25

Compound Interest (C.I.) = A – P

= Rs. 11,576.25 – Rs. 10,000 = Rs. 1,576.25

If it is compounded annually, then

Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10%, Time (n) = 1\ \frac{1}{2} years.

Amount (A) for 1 year = P\left(1+\frac{R}{100}\right)^n

= 10000\left(1+\frac{10}{100}\right)^1

= 10000\left(1+\frac{1}{10}\right)^1

= 10000\left(\frac{11}{10}\right)^1

= 10000\times\frac{11}{10}

= Rs. 11,000

Interest for \frac{1}{2} year = \frac{11000\times1\times10}{2\times100}=RS.\ 550

\therefore Total amount = Rs. 11,000 + Rs. 550 = Rs. 11,550

Now, C.I. = A – P = Rs. 11,550 – Rs. 10,000

= Rs. 1,550

Yes, interest Rs. 1,576.25 is more than Rs. 1,550.

hello guys the question is find the amount and the compound interest on rupees 10000 of for 1.5 years at 10% per annum compounded half-yearly so let's start our amount our principal is equal to 10000 and time period given is equal to 1.5 and the rate of interest that is given is 10% per annum now we have to calculate for half yearly for 6 month so hot six month this rate of interest become half become 5% and time period become double so it is 3 so using the formula a is equal to amount is equal to principal oneplus rate of interest divided by 100 power and so put the values

you will get amount amount is equal to principal that is 10000 X 1 + R is 5% / and raised to the power 3 so it become 10000 multiply 105 divided by 100 x 105 divided by 100 multiply 10 500/100 now they will cancel 21 by 20 by 50 it become 2020 21 20 so the answer is 1157 6.25 so this is the amount so this is the amount is equal to 1157 6.25 now we have to calculate the compound interest so

compound interest is equal to amount that is 1157 6.25 -10000 at is equal to 15/7 6.25 so this is our compound interest and this is our amount thank you

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