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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 $2642.90$.

comp890
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  • The increasing annuity has the same number of payments as the level annuity. – saulspatz Mar 28 '21 at 19:30
  • I'm not getting the same number as the retrospective. I don't know if something else is supposed to be added to the equation. – comp890 Mar 28 '21 at 19:35
  • Your increasing annuity has too many payments. Read my previous comment again. – saulspatz Mar 28 '21 at 19:36
  • wait wait: the 540 is wrong should be 530. and the exponents for the increasing should be 6 since you said increasing annuity has the same number of payments as the level annuity – comp890 Mar 28 '21 at 19:45
  • I'm sayin that \begin{align} 540 a_{\enclose{actuarial}{6} 0.1} + 10(Ia){\enclose{actuarial}{10} 0.1} \end{align} should be \begin{align} 540 a{\enclose{actuarial}{6} 0.1} + 10(Ia)_{\enclose{actuarial}{\color{red}{6}} 0.1} \end{align} – saulspatz Mar 28 '21 at 19:47

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