Question

find the compound interest on 32000 at 20% per annum for 2year, when compounded half- yealy​

Answer 1

Answer:

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Step-by-step explanation:

Here given that the principal amount P=P= Rs. 32,00032,000, rate of interest R=20%R=20% per annum and time T=1T=1 year. Also given that the interest is compounded half yearly (that is, six months). So, the interest paid at the end of every six months is one-half of the rate of interest per annum. So, the rate of annual interest is R=202%=10%R=202%=10% and the number of years is doubled. That is, T=2T=2 half years.

Now we are going to find the amount for 11 year by using the formula A=P(1+R100)TA=P(1+R100)T where PP is principal amount, RR is rate of annual interest and TT is time in half years.

Now we are going to substitute the values of PP, RR and TT in the formula of amount for 11 year.

Therefore, A=32000(1+10100)2A=32000(1+10100)2

⇒⇒ A=32000(100+10100)2A=32000(100+10100)2

⇒⇒A=32000(110100)2=32000(1110)2=32000(121100)A=32000(110100)2=32000(1110)2=32000(121100)

⇒⇒ A=320×121A=320×121 == Rs. 3872038720

Now we will find compound interest by subtracting the principal amount PP from the amount AA.

Therefore, compound interest (CI) == A−PA−P

⇒⇒ Compound interest (CI) == 38720−3200038720−32000 == Rs. 67206720.

Therefore, the compound interest is Rs. 67206720 for T=1T=1 year.