Algebra 1

Jane needs a short-term loan to buy a new washing machine. She needs to borrow $1500 at 20% compounded annually and plans to have it paid off in 1 year. Jane writes the formula 1500(1.2)t and finds out that this loan will cost her $1800. Which equation shows how Jane can rewrite the formula to find the annual percentage rate that would cost her the same amount if it compounded semi-annually?

I got the answer A= 1500 (1.095) is that correct?

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  1. 1500 * 1.20 = 1500 x^2 (multiply twice by half rate 1+x)
    1.20 = x^2
    x = 1.09545
    so .095 is the rate for HALF a year
    annual rate is 0.19 or 19%

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  2. So was this answer not correct? because I know see there's a 1/2t and a 2t besides two of the answer choices

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  3. let the semiannual rate be i
    then
    1500(1+i)^2 = 1800
    (1+i)^2 = 1.2 <----- Damon used x instead of 1+i, same thing
    1+i = √1.2 = 1.095445...
    i = .095445.. ----> 2i = .19089..
    so the equivalent rate is 19.089% per annum, compounded semi-annually

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  4. So, is that the answer or...?

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