# 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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