# Thread: Linear/Nonlinear Equations--compute for monthly repayments

1. ## Linear/Nonlinear Equations--compute for monthly repayments

$10,000 loan to be paid over 4 years at various interest rates: Monthly Payments is$242.51 for interest rate of 8%
$244.75 for interest rate of 8.5 % Question: Find the monthly payment when interest rate is 8.25% What interest rate would require a monthly payment of$255?

2. Hello, noreen_cruz!

I have issues with this problem.

[1] You have been given the Amortization Formula?
. . .And you're expected to manipulate it algebraically? . . . in Grade 9 ?

[2] I don't agree with their numbers.

$10,000 loan to be paid over 4 years. Monthly Payments is: .$\displaystyle \begin{array}{c}\text{\$242.51 for interest rate of 8\%} \\ \text{\$244.75 for interest rate of 8.5\%} \end{array}$(a) Find the monthly payment when interest rate is 8.25% (b) What interest rate would require a monthly payment of$255?

Amortization Formula: .$\displaystyle A \;=\;P\,\frac{i(1+i)^n}{(1+i)^n-1}$

. . where: .$\displaystyle \begin{Bmatrix}A &=&\text{periodic payment} \\ P &=& \text{principal} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

For the 8% loan, we have: .$\displaystyle P = 10,\!000,\;\;i = \tfrac{0.08}{12}.\;\;n = 48$

Then: .$\displaystyle A \;=\;10,\!000\,\frac{\left(\frac{0.08}{12}\right)\ left(1+\frac{0.08}{12}\right)^{48}} {\left(1 +\frac{0.08}{12}\right)^{48} -1} \;=\;244.1292263 \;\approx\;\boxed{\$244.13}\;\hdots\;\text{ not }\$242.51$

So I don't trust the author(s) of this problem . . .
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