Kevin takes out a $10$-year loan of $L$, which he pays by the amortization method at an annual effective interest rate of $i$. Kevin makes payments of $1000$ at the end of each year. The total amount of interest repaid during the life of the loan is also equal to $L$. Calculate the amount of interest repaid during the first year of the loan.
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My question is simple, why couldn't I use this equation for total interest instead of the correct one above: $L(1+i)^{10}-L=L$ ? I think $L(1+i)^{10}$ is the accumulated value after $10$ years and if we subtract the original loan amount $L$ from it, we should get the total amount of interest, right? However, the answer indicates that I am wrong. And I am so confused right now. Someone please help!