Question

The C.I on ₹16000 for 1.5 years at 10% p.a payable half- yearly is__?​

Answer 1

Answer:

sorry I don't know answer

Answer 2

Answer:

Step-by-step explanation:

Hint: Find the half yearly interest rate on the amount. Convert 112 years into half years and use the fact that if an amount P is compounded half-yearly with half yearly interest rate to be r for n half years, then the amount after n half years is given by A=P(1+r)n. Use the fact that the interest I is given by I=A−P. Hence find the interest on the given amount.

Complete step by step answer:

In the question the interest is levied on Rs 16000. Hence, we have P = 16,000

Also, we have rate of interest r=10%p.a

Hence, we have

r=102%=5% half-yearly

Also, we have 112 years = 32 years = 32×2 half years = 3 half years

Hence, we have n=3 half years

We know that if an amount P is compounded half-yearly with half yearly interest rate to be r for n half years, then the amount after n half years is given by A=P(1+r)n.

Hence, we have

A=P(1+r)n=16000(1+5100)3=16000×(1.05)3=18522

We know that if A is the total amount and P is the principle, then the interest is given by I=A−P

Hence, we have

I=18522−16000=2522

Hence the interest on the given amount after 112 years at 10% per annum compounded half yearly is Rs 2522.

Hence option b is correct.

Note: Alternative Solution: We calculate the amount at the end of each half year and hence calculate the total interest.

For the first half year, we have

P=16000,r=10%,t=12

We know that I=P×r×t100

Hence, we have

I=16000×10×12×100=800

For the second half year, we have

P=16000+800=16800,r = 10% and t=12

Hence, we have

I=16800×10×12×100=840

For the third half year, we have

P=16800+840=17640, r = 10% and t=12

Hence, we have

I=17640×10×12×100=882

Hence the total interest is =800+840+882=2522, which is the same as obtained above.

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