### Should You Migrate to the New Ujrah Scheme for Your PTPTN Loan?

My wife recently asked me whether or not she should participate in the new ujrah scheme as announced by PTPTN. First of all, for new contracts, the introduction of the ujrah scheme at 1% per annum would definitely save the student some interest. For example, for a given loan amount to be repaid in 180 months, the ujrah of 1% is approximately equivalent to an compound interest rate of 1.9%. Thus this scheme save the student 1.1% per annum.

However, for the old contracts signed-off before 2008, the situation is a little bit tricky, and PTPTN offers no guide to the graduated students. To close this gap, I developed a simple criterion to assist her in decision making. And the answer can be yes or no, depending on your current debt level and your remaining repayment periods.

First of all, the total amount of monies to be repaid to PTPTN, if you choose to participate in the Ujrah scheme can be calculated as:
$$T_{\rm ujrah} = P'' + P'' \cdot 180 \cdot \tfrac{1\%}{12} - \Delta P = \tfrac{23}{20}P'' - \Delta P$$
where $P''$ is your reduced balance as of June 1, 2008 (datum), $\Delta P$ is difference between your reduced balance as of now and that of datum.

However, if you you choose to stay with the original compound interest scheme, the total amount of monies to be repaid (3% annual interest over a period of $m$ months) is:
$$T = \frac{m(P'' - \Delta P)\left(1+\frac{3\%}{12} \right)^m \left(\frac{3\%}{12}\right)}{\left(1+\frac{3\%}{12}\right)^m-1} = \frac{\frac{m}{400}\left(P''-\Delta P\right)\left(\frac{401}{400}\right)^m}{\left(\frac{401}{400}\right)^m - 1}$$
For the migration to be meaningful, the total amount of monies repaid under the Ujrah scheme must be less than that of the original compound interest scheme, thus we must have the following inequality:
$$\frac{\frac{m}{400}}{1-\left(\frac{400}{401}\right)^m} \ge 1 + \frac{3}{20(1-\lambda)}, \quad \lambda = \tfrac{\Delta P}{P''}$$
From this inequality, we can rearrange and formulate a criterion to decide whether or not you should migrate to the new scheme:
$$\lambda \le \varphi(m), \quad \varphi(m) = 1 - \frac{\frac{3}{20}}{\frac{\frac{m}{400}}{1-\left(\frac{400}{401}\right)^m}-1}$$
For example, suppose your reduced balance on June 1, 2008 is RM22,500 and your reduced balance as of now is RM16,000. Then $\lambda = \frac{22,500-16,000}{22,500}=0.289$. Suppose you plan to settle your debt within 140 months, then $\varphi(140) = 0.195$. Since 0.195 < 0.289, it would be unwise to switch to the Ujrah scheme now.