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?
Don't know what your question "shows" but the initial equation would be
Amount = 1500(1.2)^t
= 1500(1.2)^1 = 1800
let the new rate be i per half-year
then
1500(1 + i)^2 = 1800
(1+i)^2 = 1.2
take √ of both sides
1+i = 1.0954..
i = .0954..
the rate is 19.09% per annum, compounded semi-annually
match this with whatever you have showing.