I doing some work on a client website, however I'm finding it difficult to calculate the correct interest amount.
- I have the principle amount, for example £200
- The loan is repaid over 3 months in monthly instalments
- I have an annual interest rate 264% (fixed), so a monthly interest rate is 22%
- The loan is repayable in equal instalments
I want to calculate the monthly repayment amount
Interest is only payable on the outstanding balance, so on the first payment:
Balance = starting balance + interest - repayment
I can work out interest ok, but I'm unsure of the work out the repayments so the balance can be reduced accordingly.
Anyone help?
Let $x$ be the starting loan amount, and $d$ be the monthly interest expressed as a decimal (i.e. $22$% interest would be $d = 1.22$ so that multiplying by $d$ corresponds to adding $22$% of interest).
We are looking to find $y$ where $y$ is a fixed payment per month subject to:
$$ d\cdot\left(d\cdot\left((d\cdot x) -y\right)-y\right)-y = 0 $$
Expressing this equation as an equation in terms of $y$ gives
$$d^3x-d^2y-dy-y = 0$$
So $$y = \frac{d^3x}{1+d+d^2}$$
With a starting value of $200$ and monthly interest of $22$%, this becomes
$$y=\frac{1.22^3 \times 200}{1+1.22+1.22^2}\approx 97.93$$