formula to calculate the monthly repayments of this contract

Question

I know that the interest rate is constant through the whole period and the interest method is declining balance. By declining balance mean that the interest at period t is calculated on the balance of period t. In the table below, interest of the 1st repayment is base on the 2748 and the interest of the second repayment is based on 2299.555.

Details :
Loan amount borrowed = 2748 The column principal = the part of the principal repaid in each period.

So far I've come up with this

 |   Date   |Principal|Balance |PayInt|#DaysPM|IntRate0|
0|26/01/2011|         |        |      |       |        |        | 
1|20/02/2011|448.445  |2748    |25    |31     |1.33%   |
2|20/03/2011|446.759  |2299.555|28    |28     |1.667%  |
3|20/04/2011|454.205  |1852.796|31    |31     |1.667%  |
4|20/05/2011|461.775  |1398.591|30    |30     |1.667%  |
5|20/06/2011|469.471  |936.816 |31    |31     |1.667%  |
6|20/07/2011|467.345  |467.345 |30    |30     |1.667%  |

Definition:

PayInt = # Interval between payment in days
IntRate0 = $\frac{Interest_t}{Balanct_t}$

The interest is supposed to be constant and 1.33% was obtained by 1.66%*$\frac{24}{30}$

I just would like to know if there is a formula to calculate the monthly repayments of this contract.

Thanks

Answer 1

If the interest compounds once per month, not once per day, the formula would be

$L_t = L_{t-1} + RL_{t-1} - P$
Where $L_t$ is the loan balance at month $t$ ($L_0$ being the original amount), $R$ is the monthly interest rate and $P$ is the monthly installment(which you don't seem to have divulged), and the payment to interest is $RL_{t-1}$ (which you seem to have also not divulged)

so the payment to principal for month $t$ will be

$P_{pt} = P - RL_{t-1}$

And the monthly installment from the given information is

$P = P_{pt} + RL_{t-1}$

Assuming the monthly rate is constant, we can select any 2 adjacent months with the same installment amount:

$P_{p1} + RL_0 = P_{p2} + RL_1$

and solve for $R$

$R = \frac{P_{p2} - P_{p1}}{L_0 - L_1}$

Substitute $L_0-P_{p1}$ for $L_1$ (thank you @DJJ) to get

$R = \frac{P_{p2} - P_{p1}}{P_{p1}}$

Which should give the monthly rate, multiply by 12 to get the APR.

If the interest compounds daily, the monthly rate would be

$R = (1 + \frac{r}{n})^n - 1$

where $r$ is the daily rate and $n$ is the number of days in the month.

Edit:

With the new data you have posted (the interest payments), your APR is 20% ($1\frac{2}{3} * 12$), with the first month being $\frac{4}{5}$ (24 days out of 30) of the regular monthly rate