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A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is 
    Correct answer is '16000'. Can you explain this answer?
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    A person invested a certain amount of money at 10% annual interest, co...
    Let the sum be P. 
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    A person invested a certain amount of money at 10% annual interest, co...
    Given:

    • Rate of interest = 10% per annum

    • Interest is compounded half-yearly

    • After one and a half years, interest and principal together became Rs 18522



    To find: The amount invested

    Approach:

    • Let the amount invested be P

    • Rate of interest per half-year = 10%/2 = 5%

    • Time period = 1.5 years = 3 half-years

    • Using the formula for compound interest: A = P(1 + R/100)n

    • Where A is the amount after n years, P is the principal, R is the rate of interest and n is the number of years

    • After 3 half-years, the amount will be: P(1 + 5%/100)3 = P(1.05)3

    • Given that the total amount after 1.5 years is Rs 18522

    • Therefore, P(1.05)3 = 18522

    • Solving for P, we get: P = 16000



    Answer: The person had invested Rs 16000.
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