I'm learning about the prospective for loan repayment but I'm having trouble creating the equation. Here was my problem (loan repayment- finding the loan if end payment increases by certain amount)
I'm finding the outstanding balance after the fourth payment using the prospective method.
I learned that both prospective and retrospective methods give the same answer but with different equations.
If I used retrospective I should get $3301.20(1.1)^4 - 500(1.1)^3 -510(1.1)^2 -520(1.1) -530 = 2448.68$
the prospective method is done by calculating the outstanding balance by looking to future payments. I tried doing a similar method when getting the loan where $10-4=6$ payments left on the loan
$$\require{enclose} \begin{align} 540 a_{\enclose{actuarial}{6} 0.1} + 10(Ia)_{\enclose{actuarial}{10} 0.1} = 540\left(\frac{1-\left(\frac{1}{1.1}\right)^6}{0.1}\right)+10\left(\frac{\frac{1-\left(\frac{1}{1.1}\right)^{10}}{\frac{0.1}{1.1}}-10\left(\frac{1}{1.1}\right)^{10}}{0.1}\right) \end{align}$$
but I'm getting a $2642.90$.