Back of the envelope home loan calculations - Part II

In the previous post, I wrote about a simple way of finding the amount, one ends repaying when s/he avails the loan. In this post I am going to write about should one dip into savings or avail the maximum limit of the loan? This was asked to me a few months back and that's when I started thinking about it.

My friend was in a unique position that he had more home loan eligibility than he had a requirement for. Not many are lucky, the way he was. When he asked me whether he should dip into his savings or avail the full loan limit I had no answer. I promised to get back to him after doing my homework and it was interesting when the answer revealed itself.

As usual, let's put in some numbers and do the calculation. Let's say, my friend needed INR 50L and he had a saving of about 12L. Lets assume his loan eligibility is also INR 50L. Now the question becomes, should he take a loan of full 50L INR or opt for a loan of 38L and use his savings worth 12L? In both cases, he would spend INR 50L.

For the sake of simplicity, the calculations are done with the following assumptions

1. Tenure of the loan is 20 years.
2. Rate of interest for Loan and Savings will remain unchanged for entire tenure.
3. Rate of interest payable on Loan and receivable on Savings is equal.
4. Things like tax benefits on housing loan and tax payable on savings interest etc is kept out of consideration for simplicity of calculations.
5. Savings are compounded for entire duration of the tenure and there is no withdrawal during the service period of the loan.

Lets consider a rate of interest band between 6% and 14% which are typical for home loan and fixed deposit rates. Also, for making the analysis more interesting lets vary the Savings corpus that my friend held.

To recap,

• Loan Amount = INR 50L
• Savings = Varying between 5L and 15L INR
• Savings calculation Method = Compound interest calculated yearly
• Rate if interest for both Loan and Savings = Varied between 6% and 14%

Total amount paid to close the loan is based on this table (and explained in the previous post, Back of the envelope home loan calculations)

Table 1:- Amount repayable across varying rates

Hence amount repaid at 6% rate for 20-years is 50L x 1.72, at 7% is 50L x 1.86, ... so on and so forth. Comparing loan amount paid to amount received by investing the savings for a return of between 6% to 14% gives a clear picture which helps in answering our original question.

Figure 1:- Amount Paid v/s amount earned over 20-year tenure

The dark red color shows the loan amount repaid at various interest rates whereas the other lines display trend for different savings amount over the same set of varied interest rates.In my friend's case (Orange Line) where the Savings corpus was 12L, the red curve and the orange curve meet at the 13% mark and overtakes loan curve at 14% mark. This means that if my friend can manage to compound his savings at a rate of 13% or more he will have earned more money than spent on repaying loan. Note that for higher savings corpus , the need for savings growth requirement gets moderated to ~12% in order to stay in green.

Looking at the chart my friend made his decision. You will have to make yours.

The rule of thumb guidelines are as follows

1. If your Savings corpus is 30% or more of your loan amount and your loan / savings rate is in double-digits, one may benefit by retaining the saving and availing the full loan eligibility
2. If your Saving, is <20% of your loan amount, it almost always makes sense to use your savings and draw lesser amount in loan (or repay immediately)
3. If your Savings is between 20% and 30% of your loan amount, then its game-on. If you are able to grow your money at a higher compound rate than your loan rate, you win, else you lose.

Hope this post has been able to explain the dynamics of money and equipped you to make more informed decisions.

Adios Amigos !